Updated on 2024/10/24

Information

 

写真a

 
MASATO TSUJII
 
Organization
Faculty of Mathematics Division of Analysis Professor
School of Sciences Department of Mathematics(Concurrent)
Graduate School of Mathematics Department of Mathematics(Concurrent)
Joint Graduate School of Mathematics for Innovation (Concurrent)
Title
Professor
Profile
My research area is dynamical system theory(the qualitative theory of ordinary differential equations) and ergodic theory. I study transfer operators associated to chaotic dynamical systems by using methods of functional analysis such as Fourier analysis and semi-classical analysis. My main target of research now is the geodesic flows on negatively curved manifold, which is a type of chaotic hyperbolic flow, and the corresponding transfer operators and semi-calsscial zeta funtions. From April 2022, I have been working as the dean of Faculty of Mathematics, Graduate school of Mathematics and Joint Graduate school of Mathematics-for-Innovation. For education, I gave a few lectures such as calculus, linear algebra, comlex function theory, dynamical system theory, etc) and supervised a few students in their studies of mathematics.
Homepage

Research Areas

  • Natural Science / Mathematical analysis

  • Natural Science / Basic mathematics

  • Natural Science / Applied mathematics and statistics

Degree

  • Doctoral degree of Science

Research History

  • Kyushu University Faculty of Mathematics Professor 

    2007.2 - Present

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    Country:Japan

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  • 東京工業大学 助手 1993. 10. 1 -- 1996.7.31 北海道大学 助教授 1996.8.1 -- 2007.2.14   

Research Interests・Research Keywords

  • Research theme: 力学系理論

    Keyword: 力学系理論

    Research period: 2024

  • Research theme: Dynamical System Theory

    Keyword: Dynamical System Theory

    Research period: 2024

  • Research theme: Exponential mixing of Anosov flows and problems in quantum chaos

    Keyword: Quantum chaos, Anosov flow, geodesic flow

    Research period: 2021.4

  • Research theme: Spectral study of transfer operators for hyperbolic dynamical systems

    Keyword: Dynamical Systems, Transfer operators

    Research period: 2016.4 - 2020.3

  • Research theme: Transfer operators for geodesic flows and the semi-classical zeta function

    Keyword: geodesic flow, transfer operators, the semi-classical zeta functions

    Research period: 2010.4 - 2015.3

  • Research theme: Functional analytic methods in dynamical systems theory

    Keyword: hypebolic dynamical systems, transfer operators, dynamical zeta functions

    Research period: 2006.4 - 2010.3

Awards

  • 日本数学会 JMSJ論文賞(2018年度)

    2019.3   日本数学会  

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    Exponential mixing for volume-preserving Anosov flows in dimension 3.

  • 日本数学会 秋季賞(2013年度)

    2013.9   日本数学会  

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    微分可能力学系のエルゴード理論における関数解析的手法

Papers

  • On bifurcation of statistical properties of partially hyperbolic endomorphisms

    Masato Tsujii, Zhiyuan Zhang

    Ergodic Theory and Dynamical Systems   44 ( 3 )   933 - 944   2024.3   ISSN:0143-3857 eISSN:1469-4417

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    Language:Others   Publishing type:Research paper (scientific journal)   Publisher:Ergodic Theory and Dynamical Systems  

    We give an example of a path-wise connected open set of partially hyperbolic endomorphisms on the -torus, on which the (unique) Sinai-Ruelle-Bowen (SRB) measure exists for each system and varies smoothly depending on the system, while the sign of its central Lyapunov exponent changes.

    DOI: 10.1017/etds.2023.11

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  • Smooth mixing Anosov flows in dimension three are exponentially mixing. Reviewed International journal

    Masato Tsujii, Zhiyuan Zhang

    Annals of Math.   197 ( 1 )   65 - 158   2023.1

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    3次元のアノソフ流が位相混合的であるならば指数混合的であることを示した。

  • Invariant densities for random continued fractions Reviewed International journal

    Carlene Kalle, Valentin Matache, Evgeny Verbitskiy

    Journal of Mathematical Analysis and Applications, Vol. 512, No.2, (2022)   512 ( 2 )   2022.5

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Geodesic flows of negatively curved manifolds and the semi-classical zeta function Invited Reviewed International journal

    Masato Tsujii

    Sugaku   18   69 - 92   2018.10

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    Language:English  

    DOI: 10.1090/suga/429

  • The error term in the prime orbit theorem for expanding semiflows Reviewed International journal

    Masato Tsujii

    Ergodic Theory and Dynamical Systems   38 ( 5 )   1954 - 2000   2018.8

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    Language:English   Publishing type:Research paper (scientific journal)  

    We consider suspension semiflows of angle-multiplying maps on the circle and study the distributions of periods of their periodic orbits. Under generic conditions on the roof function, we give an asymptotic formula on the number of prime periodic orbits with period . The error term is bounded, at least, by for arbitrarily small ϵ>0, where and are, respectively, the topological entropy and the maximal Lyapunov exponent of the semiflow.

    DOI: 10.1017/etds.2016.113

  • Exponential mixing for generic volume-preserving Anosov flows in dimension three Reviewed International journal

    Tsujii Masato

    Journal of the Mathematical Society of Japan   70 ( 2 )   757 - 821   2018.4

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    アノソフ流は生成的な条件の下で指数混合的であろうという長年の予想について、3次元の体積保存系の場合に肯定的に解決した。

    DOI: 10.2969/jmsj/07027595

  • The semiclassical zeta function for geodesic flows on negatively curved manifolds Reviewed

    Frederic Faure, Masato Tsujii

    INVENTIONES MATHEMATICAE   208 ( 3 )   851 - 998   2017.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    We consider the semi-classical (or Gutzwiller-Voros) zeta functions for contact Anosov flows. Analyzing the spectra of the generators of some transfer operators associated to the flow, we prove that, for arbitrarily small , its zeros are contained in the union of the -neighborhood of the imaginary axis, , and the half-plane , up to finitely many exceptions, where is the hyperbolicity exponent of the flow. Further we show that the density of the zeros along the imaginary axis satisfy an analogue of the Weyl law.

    DOI: 10.1007/s00222-016-0701-5

  • On the Fourier transforms of self-similar measures Reviewed International journal

    Tsujii Masato

    Dynamical Systems – an international journal   2015.11

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Prequantum transfer operator for symplectic anosov diffeomorphism Reviewed

    Frédéric Faure, Tsujii Masato

    Asterisque   2015-January ( 375 )   1 - 237   2015.1

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    Language:English   Publishing type:Research paper (scientific journal)  

    We define the preauantization of a symplectic Aaosov diffeoniorphism f : M -∗ M as a U(l) extension of the diffeoniorphism / preserving a connection related to the symplectic structure on M. We study the spectral properties of the associated transfer operator with a given potential V € C°° (M), called prequantum transfer operator. This is a model of transfer operators for geodesic flows on negatively curved manifolds {or contact Anosov flows). We restrict the prequantum transfer operator to the JV-the Fourier mode with respect to the U(l) action and investigate the spectral property in the limit N -∗ oo, regarding the transfer operator as a Fourier integral operator and using semi-classical analysis. In the main result, under some pinching conditions, we show a "band structure" of the spectrum, that is, the spectrum is contained in a few separated annuli and a disk concentric at the origin. We show that, with the special (Holder continuous) potential Vo = 1/2log|det Df|Eu|1, where £ is the unstable subspace, the outermost annulus is the unit circle and separated from the other parts. For this, we use an extension of the transfer operator to the Grassmanian bundle. Using Atiyah-Bott trace formula, we establish the Gutzwiller trace formula with exponentially small reminder for large time. We show also that, for a potential V such that the outermost annulus is separated from the other parts, most of the eigenvalues in the outermost annulus concentrate on a circle of radius exp((V - V0)) where (.) denotes the spatial average on M. The number of the eigenvalues in the outermost annulus satisfies a Weyl law, that is, NdVol (M) in the leading order with d = 1/2dimM. We develop a semiclassical calculus associated to the prequantum operator by defining quantization of observables OpN (Ψ) as the spectral projection of multiplication operator by Ψ to this outer annulus. We obtain that the semiclassical Egorov formula of quantum transport is exact. The correlation functions defined by the classical transfer operator are governed for large time by the restriction to the outer annulus that we call the quantum operator. We interpret these results from a physical point of view as the emergence of quantum dynamics in the classical correlation functions for large.

  • Geodesic flows on negatively curved manifolds and the semi-classical zeta function Reviewed International journal

    Tsujii Masato

    日本数学会   2014.7

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  • Band structure of the Ruelle spectrum of contact Anosov flows Reviewed International journal

    Tsujii Masato

    COMPTES RENDUS MATHEMATIQUE   351 ( 9-10 )   385 - 391   2013.5

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    Language:English   Publishing type:Research paper (scientific journal)  

    If X is a contact Anosov vector field on a smooth compact manifold M and V∈C∞(M), it is known that the differential operator A=-X+V has some discrete spectrum called Ruelle-Pollicott resonances in specific Sobolev spaces. We show that for |Imz|→∞ the eigenvalues of A are restricted to vertical bands and in the gaps between the bands, the resolvent of A is bounded uniformly with respect to |Im(z)|. In each isolated band, the density of eigenvalues is given by the Weyl law. In the first band, most of the eigenvalues concentrate to the vertical line Re(z)=*D〉M, the space average of the function D(x)=V(x)-12divX|Eu(x) where Eu is the unstable distribution. This band spectrum gives an asymptotic expansion for dynamical correlation functions. Si X est un champ de vecteur d'Anosov de contact sur une variété compacte lisse M et si V∈C∞(M), il est connu que l'opérateur différentiel A=-X+V a un spectre discret appelé résonances de Ruelle-Pollicott dans des espaces de Sobolev spécifiques. On montre que, pour |Imz|→∞, les valeurs propres de A sont incluses dans des bandes verticales et que, dans les gaps entre ces bandes, la résolvante de A est bornée uniformément par rapport à |Im(z)|. Dans chaque bande isolée, la densité des valeurs propres est donnée par une loi de Weyl. Dans la première bande, la plupart des valeurs propres se concentrent sur la ligne verticale Re(z)=*D〉M, qui est la moyenne spatiale de la fonction D(x)=V(x)-12divX|Eu(x), où Eu est la distribution instable. Ce spectre en bande permet d'exprimer le comportement asymptotique des fonctions de corrélations dynamiques. © 2013 .

    DOI: 10.1016/j.crma.2013.04.022

  • Contact Anosov flows and the Fourier–Bros–Iagolnitzer transform Reviewed International journal

    Tsujii Masato

    Ergodic theory and Dynamical systems (Cambridge University Press)   32 ( 6 )   2083 - 2118   2012.10

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    This paper is about spectral properties of transfer operators for contact Anosov flows. The main result gives the essential spectral radii of the transfer operators acting on an appropriate function space exactly and improves the previous result in Tsujii [Quasi-compactness of transfer operators for contact Anosov flows. Nonlinearity 23 (2010), 1495–1545]. Also, we provide a simplified proof by using the so-called Fourier–Bros–Iagolnitzer (FBI) (or Bargmann) transform.

    DOI: http://dx.doi.org/10.1017/S0143385711000605

  • Quasi-compactness of transfer operators for contact Anosov flows Reviewed International journal

    辻井 正人

    Nonlinearity   2010.2

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Dynamical determinants and spectrum for hyperbolic diffeomorphisms Invited Reviewed International journal

    Viviane Baladi, Masato TSUJII

    "Probabilistic and Geometric Structures in Dynamics", K. Burns, D. Dolgopyat and Ya. Pesin (eds), Contemp. Math. (Amer. Math. Soc.), Volume in honour of M. Brin's 60th birthday   2008.10

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  • Decay of correlations in suspension semi-flow of angle-multiplying maps Reviewed International journal

    辻井 正人

    Ergodic Therory and Dynamical Systems (Cambridge)   2007.12

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  • Smooth mixing Anosov ows in dimension three are exponentially mixing

    Masato Tsujii, Zhiyuan Zhang

    Annals of Mathematics   197 ( 1 )   65 - 158   2023   ISSN:0003-486X eISSN:1939-8980

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    Publishing type:Research paper (scientific journal)   Publisher:Annals of Mathematics  

    We show that a topologically mixing C∞ Anosov ow on a 3-dimensional compact manifold is exponentially mixing with respect to any equilibrium measure with Holder potential

    DOI: 10.4007/annals.2023.197.1.2

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  • VIRTUALLY EXPANDING DYNAMICS

    Masato Tsujii

    Kyushu Journal of Mathematics   77 ( 2 )   291 - 298   2023   ISSN:1340-6116

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    Publishing type:Research paper (scientific journal)   Publisher:Kyushu Journal of Mathematics  

    We introduce a class of discrete dynamical systems that we call virtually expanding. This is an open subset of self-covering maps on a closed manifold which contains all expanding maps and some partially hyperbolic volume-expanding maps. We show that the Perron–Frobenius operator is quasi-compact on a Sobolev space of positive order for such a class of dynamical systems.

    DOI: 10.2206/kyushujm.77.291

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  • Invariant densities for random continued fractions

    Charlene Kalle, Valentin Matache, Masato Tsujii, Evgeny Verbitskiy

    Journal of Mathematical Analysis and Applications   512 ( 2 )   126163 - 126163   2022.8   ISSN:0022-247X eISSN:1096-0813

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    Language:Others   Publishing type:Research paper (scientific journal)   Publisher:Elsevier {BV}  

    We continue the study of random continued fraction expansions, generated by random application of the Gauss and the Rényi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous invariant measure with smooth density.

    DOI: 10.1016/j.jmaa.2022.126163

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  • The partial captivity condition for U(1) extensions of expanding maps on the circle Reviewed

    Yushi Nakano, Tsujii Masato, Jens Wittsten

    Nonlinearity   29 ( 7 )   1917 - 1925   2016.5

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    This paper concerns the compact group extension f : ⌉2→⌉2, f (x, s) = (E(x), s + τ(x) mod 1) of an expanding map E : S1→S1. The dynamics of f and its stochastic perturbations have previously been studied under the so-called partial captivity condition. Here we prove a supplementary result that shows that partial captivity is a C τ generic condition on τ, once we fix E.

    DOI: 10.1088/0951-7715/29/7/1917

  • On the Fourier transforms of self-similar measures Reviewed

    Masato Tsujii

    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL   30 ( 4 )   468 - 484   2015.10

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    For the Fourier transform mu of a general ( non- trivial) self- similar measure mu on the real line R, we prove a large deviation estimate

    DOI: 10.1080/14689367.2015.1078291

  • Semiclassical approach for the Ruelle-Pollicott spectrum of hyperbolic dynamics

    Frédéric Faure, Tsujii Masato

    Springer INdAM Series   65 - 135   2014.1

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    Uniformly hyperbolic dynamics (Axiom A) have “sensitivity to initial conditions” and manifest “deterministic chaotic behavior”, e.g. mixing, statistical properties etc. In the 1970, David Ruelle, Rufus Bowen and others have introduced a functional and spectral approach in order to study these dynamics which consists in describing the evolution not of individual trajectories but of functions, and observing the convergence towards equilibrium in the sense of distribution. This approach has progressed and these last years, it has been shown by V. Baladi, C. Liverani, M. Tsujii and others that this evolution operator (“transfer operator”) has a discrete spectrum, called “Ruelle-Pollicott resonances” which describes the effective convergence and fluctuations towards equilibrium.Due to hyperbolicity, the chaotic dynamics sends the information towards small scales (high Fourier modes) and technically it is convenient to use “semiclassical analysis” which permits to treat fast oscillating functions. More precisely it is appropriate to consider the dynamics lifted in the cotangent space T M of the initial manifold M (this is an Hamiltonian flow). We observe that at fixed energy, this lifted dynamics has a relatively compact non-wandering set called the trapped set and that this lifted dynamics on T M scatters on this trapped set. Then the existence and properties of the Ruelle-Pollicott spectrum enters in a more general theory of semiclassical analysis developed in the 1980 by B. Helffer and J. Sjöstrand called “quantum scattering on phase space”.We will present different models of hyperbolic dynamics and their Ruelle-Pollicott spectrum using this semi-classical approach, in particular the geodesic flow on (non necessary constant) negative curvature surface ℳ. In that case the flow is on M=T1∗ℳ, the unit cotangent bundle of ℳ. Using the trace formula of Atiyah-Bott, the spectrum is related to the set of periodic orbits.We will also explain some recent results, that in the case of Contact Anosov flow, the Ruelle-Pollicott spectrum of the generator has a structure in vertical bands. This band spectrum gives an asymptotic expansion for dynamical correlation functions. Physically the interpretation is the emergence of a quantum dynamics from the classical fluctuations. This makes a connection with the field of quantum chaos and suggests many open questions.

    DOI: 10.1007/978-3-319-04807-9_2

  • Contact Anosov flows and the Fourier-Bros-Iagolnitzer transform Reviewed

    Masato Tsujii

    ERGODIC THEORY AND DYNAMICAL SYSTEMS   32 ( 6 )   2083 - 2118   2012.12

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    This paper is about spectral properties of transfer operators for contact Anosov flows. The main result gives the essential spectral radii of the transfer operators acting on an appropriate function space exactly and improves the previous result in Tsujii [Quasi-compactness of transfer operators for contact Anosov flows. Nonlinearity 23 (2010), 1495-1545]. Also, we provide a simplified proof by using the so-called Fourier-Bros-Iagolnitzer (FBI) (or Bargmann) transform.

    DOI: 10.1017/S0143385711000605

  • Quasi-compactness of transfer operators for contact Anosov flows Reviewed

    Masato Tsujii

    NONLINEARITY   23 ( 7 )   1495 - 1545   2010.7

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    For any C(r) contact Anosov flow with r >= 3, we construct a scale of Hilbert spaces, which are embedded in the space of distributions on the phase space and contain all the C(r) functions, such that the one-parameter family of transfer operators for the flow extend to them boundedly and that the extensions are quasi-compact. We also give explicit bounds on the essential spectral radii of those extensions in terms of differentiability r and the hyperbolicity exponents of the flow.

    DOI: 10.1088/0951-7715/23/7/001

  • Decay of correlations in suspension semi-flows of angle-multiplying maps Reviewed

    Masato Tsujii

    Ergodic Theory and Dynamical Systems   28 ( 1 )   291 - 317   2008.2

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    We consider suspension semi-flows of angle-multiplying maps on the circle for Cr ceiling functions with r3. Under a Crgeneric condition on the ceiling function, we show that there exists a Hilbert space (anisotropic Sobolev space) contained in the L2 space such that the PerronFrobenius operator for the time-t-map acts naturally on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description of decay of correlations. Furthermore, the PerronFrobenius operator for the time-t-map is quasi-compact for a Cr open and dense set of ceiling functions.

    DOI: 10.1017/S0143385707000430

  • Anisotropic hölder and sobolev spaces for hyperbolic diffeomorphisms Reviewed

    Viviane Baladi, Masato Tsujii

    Annales de l'Institut Fourier   57 ( 1 )   127 - 154   2007.1

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    We study spectral properties of transfer operators for diffeomorphisms T : X → X on a Riemannian manifold X. Suppose that Ω is an isolated hyperbolic subset for T, with a compact isolating neighborhood V ⊂ X. We first introduce Banach spaces of distributions supported on V, which are anisotropic versions of the usual space of Cp functions Cp (V) and of the generalized Sobolev spaces Wp,t(V), respectively. We then show that the transfer operators associated to T and a smooth weight g extend boundedly to these spaces, and we give bounds on the essential spectral radii of such extensions in terms of hyperbolicity exponents.

    DOI: 10.5802/aif.2253

  • Zeta functions and dynamical systems Reviewed

    Carlangelo Liverani, Masato Tsujii

    NONLINEARITY   19 ( 10 )   2467 - 2473   2006.10

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    In this brief paper we present a very simple strategy to investigate dynamical determinants for uniformly hyperbolic systems. The construction builds on the recent introduction of suitable functional spaces which allow us to transform simple heuristic arguments into rigorous ones. Although the results so obtained are not exactly optimal, the straightforwardness of the argument makes them noticeable.

    DOI: 10.1088/0951-7715/19/10/011

  • Smoothness of solenoidal attractors Reviewed

    Artur Avila, Sébastien Gouëzel, Masato Tsujii

    Discrete and Continuous Dynamical Systems   15 ( 1 )   21 - 35   2006.5

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    We consider dynamical systems generated by skew products of affine contractions on the real line over angle-multiplying maps on the circle S 1: T-.S1 X ℝ-.S1 × ℝ, T(x,y) = (ℓx, λy +f /(x)) where ≥ 2, 0 < λ < 1 and f is a Cr function on S1. We show that, if λ 1+2s > 1 for some 0 * s < r - 2, the density of the SBR measure for T is contained in the Sobolev space Ws(S1 ×ℝ) for almost all (Crgeneric, at least) f.

    DOI: 10.3934/dcds.2006.15.21

  • Physical measures for partially hyperbolic surface endomorphisms Reviewed

    Masato Tsujii

    Acta Mathematica   194 ( 1 )   37 - 132   2005.1

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    DOI: 10.1007/BF02392516

  • Weakly expanding skew-products of quadratic maps Reviewed

    Jérôme Buzzi, Olivier Sester, Masato Tsujii

    Ergodic Theory and Dynamical Systems   23 ( 5 )   1401 - 1414   2003.10

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    We consider quadratic skew-products over angle-doubling of the circle and prove that they admit positive Lyapunov exponents almost everywhere and an absolutely continuous invariant probability measure. This extends corresponding results of M. Viana and J. F. Alvès for skew-products over the linear strongly expanding map of the circle.

    DOI: 10.1017/S0143385702001694

  • A measure on the space of smooth mappings and dynamical system theory

    Tsujii Masato

    Journal of the Mathematical Society of Japan   44 ( 3 )   415 - 425   1992.7

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    A measure on the space of smooth mappings and dynamical system theory

    DOI: 10.2969/jmsj/04430415

  • Rotation number and one-parameter Families of circle diffeo morphisms.

    Tsujii Masato

    Ergodic theory and Dynamical systems   12 ( 2 )   359 - 363   1992.1

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    We consider one-parameter families of circle diffeomorphisms, f1(x) = f(x) + t(t C0(X, X) and A X a minimal set of f. We first introduce a new topological invariant, the D-function of a minimal set, by the investigation of the decomposition of the minimal set A under the action of fn n N. Then important properties about the invariant and the existence of minimal set with a given D-function in some subshift of finite type are discussed. Finally Sharkovskii's theorem is generalized to minimal sets of continuous mappings from the interval into itself.

    DOI: 10.1017/S0143385700006805

  • Regular points for ergodic sinai measures Reviewed

    Masato Tsujii

    Transactions of the American Mathematical Society   328 ( 2 )   747 - 766   1991.12

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    Ergodic properties of smooth dynamical systems are considered. A point is called regular for an ergodic measure μ if it is generic for μ and the Lyapunov exponents at it coincide with those of μ. We show that an ergodic measure with no zero Lyapunov exponent is absolutely continuous with respect to unstable foliation [L] if and only if the set of all points which are regular for it has positive Lebesgue measure.

    DOI: 10.1090/S0002-9947-1991-1072103-1

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Books

  • 力学系入門(原著第2版)

    Hirsh, Smale, Devaney 辻井, 桐木, 谷川, 三波(Role:Joint translator)

    共立出版  2007.8 

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    Language:Japanese   Book type:Scholarly book

  • Prequantum transfer operator for symplectic Anosov diffeomorphism

    Frederic Faure and Masato Tsujii(Role:Joint author)

    フランス数学会  2015.12 

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    Language:English   Book type:General book, introductory book for general audience

Presentations

  • 3-dimensional Anosov flows Invited International conference

    辻井 正人(本人)

    Spring School on Transfer operator  2021.3 

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    Event date: 2021.3

    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:研究室(オンライン)   Country:Switzerland  

    Bernoulli center

    Other Link: https://cib.epfl.ch/events/1508

  • Large Deviations Principle for S-unimodal maps Invited International conference

    辻井 正人

    Real and Complex dynamics of Henon maps  2019.11 

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    Event date: 2019.11

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Paris Observatory   Country:France  

    I will speak about a recent joint-work with Hiroki Takahasi (Keio Univ.), in which we proved the Large Deviations Principle of Level 2 (LDP2) for ALL S-unimodal maps. This work is based on a recent work by Chung, Rivera-Letelier and Takahasi, where the LDP2 is proved for any non- renormalizable S-unimodal maps. To extend LDP2 to all S-unimodal maps, we provided some analysis on the process where orbits on a renormalization cycle fall in a deeper cycle. I will also give a counter-example of a bi-modal cubic map for which LDP2 does not hold.

    Other Link: http://henon-fr-jp.imj-prg.fr

  • COHOMOLOGICAL THEORY OF THE SEMI-CLASSICAL ZETA FUNCTIONS Invited International conference

    Masato Tsujii

    Dynamics, Equations and Applications 2019  2019.9 

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    Event date: 2019.9

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:AGH, Krakow   Country:Poland  

    We first review very briefly about recent developments in analysis of transfer operators for hyperbolic dynamical systems. We will then focus on the semi-classical (or Gutzwiller-Voros) zeta functions for geodesic flows on negatively curved manifolds. We show that the semi-classical zeta function is the dynamical Fredholm determinant of a transfer operator acting on the leaf-wise cohomology space along the unstable foliation. This realize the idea presented by Guillemin and Patterson a few decades ago. As an application, we see that the zeros of the semi-classical zeta function concentrate along the imaginary axis, imitating those of Selberg zeta function.

  • Transfer operators for Anosov diffeomorphisms Invited International conference

    Masato Tsujii, Vivian Baladi

    Beyond Uniform Hyperbolicity 2019  2019.7 

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    Event date: 2019.7

    Language:English   Presentation type:Oral presentation (general)  

    Venue:CIRM Marseille   Country:France  

    We present a functional-analytic approach to the study of transfer operators for Anosov flows. To study transfer operators, a basic idea in semi-classical analysis suggests to look at the action of the flow on the cotangent bundle. Though this idea is simple and intuitive (as we will explain in the lectures), we need some framework to make it work. In the lectures, we present such a framework based on a wave-packet transform.

  • Exponential mixing for volume-preserving Anosov flows Invited International conference

    辻井 正人

    Real and Complex dynamics of Henon maps  2019.3 

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    Event date: 2019.3

    Language:English   Presentation type:Oral presentation (general)  

    Venue:慶應義塾大学   Country:Japan  

  • On cohomological theory of dynamical zeta functions Invited International conference

    辻井 正人

    Dynamical Systems and Related Topics  2018.8 

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    Event date: 2018.8

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Federal university of Salvador   Country:Brazil  

  • Gutzwiller-Voros zeta functions for geodesic flows on negatively curved manifolds Invited International conference

    辻井 正人

    The third international conference on the dynamics of differential equations  2017.12 

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    Event date: 2017.12 - 2016.12

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:広島大学   Country:Japan  

  • On cohomological theory of dynamical zeta functions Invited International conference

    辻井 正人

    Spectral geometry, graphs and semiclassical analysis  2017.12 

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    Event date: 2017.12 - 2016.12

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Aussois   Country:France  

  • Exponential decay of correlations for Anosov flows Invited International conference

    辻井 正人

    Analytical aspects of hyperbolic flows  2017.7 

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    Event date: 2017.7 - 2016.7

    Language:English   Presentation type:Oral presentation (general)  

    Venue:The university of Tokyo   Country:France  

  • The spectrum of semi-classical transfer operator for expanding-semi flows Invited International conference

    辻井 正人

    Tokyo–Berkeley Mathematics Workshop Partial Differential Equations and Mathematical Physics  2017.1 

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    Event date: 2017.1 - 2016.1

    Language:English   Presentation type:Oral presentation (general)  

    Venue:The university of Tokyo   Country:Japan  

  • Exponential mixing for generic volume-preserving Anosov flows in dimension three Invited International conference

    辻井 正人

    Analytical Methods in Classical and Quantum Dynamical Systems  2016.7 

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    Event date: 2016.6 - 2016.7

    Language:English   Presentation type:Oral presentation (general)  

    Venue:The Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy   Country:Japan  

  • Exponential mixing for generic volume-preserving Anosov flows in dimension three Invited International conference

    辻井 正人

    Mixing flows and averaging method  2016.4 

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    Event date: 2016.4 - 2016.5

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Erwin Schrodinger Institute, Vienna, Austria   Country:Japan  

    Other Link: http://www.esi.ac.at/activities/events/2016/mixing-flows-and-averaging-methods

  • The spectrum of semi-classical transfer operator for expanding semi-flows with holes International conference

    辻井 正人

    Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism  2016.3 

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    Event date: 2016.3

    Language:English  

    Venue:ICERM, Brown university   Country:Japan  

    Other Link: https://icerm.brown.edu/programs/sp-s16/w2/

  • The error term of The prime Orbit Theorem for expanding semi-flows Invited International conference

    Tsujii Masato

    School and Conference on Dynamical Systems  2015.8 

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    Event date: 2015.7 - 2015.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:ICTP, Trieste, Italy   Country:Italy  

    Other Link: http://indico.ictp.it/event/a14293/

  • Resonances for geodesic flows on negatively curved manifolds Invited International conference

    Tsujii Masato

    国際数学者会議(ICM2014)  2014.8 

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    Event date: 2014.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Coex, Seoul   Country:Korea, Republic of  

    We report some recent progress in the study of geodesic flows on negatively curved manifolds (or more generally contact Anosov flows). We consider one-parameter groups of transfer operators associated to the flows and investigate the spectra of their generators. The main ingredients are the recent results about a band structure of the discete spectrum, which are obtained in the authors’ joint works.

  • Spectrum of transfer operators for expanding semi-flows. International conference

    Tsujii Masato

    国際数学者会議(ICM2014)サテライト会議 Dynamical systems and related topics  2014.8 

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    Event date: 2014.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:忠南大学, Seoul   Country:Korea, Republic of  

  • Geodesic flows on negatively curved manifolds and the semi-classical zeta function Invited International conference

    辻井 正人

    Measurable and Topological Dynamical Systems, Keio 2013  2013.12 

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    Event date: 2013.12

    Language:English   Presentation type:Oral presentation (general)  

    Venue:慶応大学   Country:Japan  

    We consider the semi-classical (or Gutzwiller-Voros) zeta functions for &#36;C^infty&#36; contact Anosov flows. Analyzing the spectra of the generators for some transfer operators associated to the flow, we prove, for any &#36; au>0&#36;, that its zeros are contained in the union of the &#36; au&#36;-neighborhood of the imaginary axis, &#36;|Re(s)|< au&#36;, and the region &#36;Re(s)<-chi_0+ au&#36;, up to finitely many exceptions, where &#36;chi_0>0&#36; is the hyperbolicity exponent of the flow.
    Further we show that the zeros in the neighborhood of the imaginary axis satisfy an analogue of the Weyl law.

    Other Link: http://www.math.keio.ac.jp/~nakada/dynamical_systems_2013-dec/program.pdf

  • Spectrum of geodesic flow on negatively curved manifold Invited International conference

    Tsujii Masato

    Hyperbolicity and Dimension  2013.12 

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    Event date: 2013.12

    Language:English   Presentation type:Oral presentation (general)  

    Venue:CIRM, Marseille   Country:France  

    We consider the one-parameter families of transfer operators for geodesic flows on negatively curved manifolds. We show that the spectra of the generators have some "band structure" parallel to the imaginary axis. As a special case of "semi-classical" transfer operator, we see that the eigenvalues concentrate around the imaginary axis with some gap on the both sides. Those eigenvalues appear as the zeros of the so-called semi-classical (or Gutzwiller-Voros) zeta functions. These results are obtained as application of some ideas in the semi-classical analysis.

    Other Link: http://hasselblatttroubetzkoy.weebly.com/information1.html

  • The semi-classical zeta function Invited International conference

    Tsujii Masato

    ICTP-ESF School and Conference in Dynamical Systems  2012.6 

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    Event date: 2012.6

    Language:English   Presentation type:Oral presentation (general)  

    Venue:ICTP, Trieste   Country:Italy  

    We discuss about analytic properties of the so-called semi-classical zeta functions for geodesic flows on the closed manifold with negative sectional curvature. The main results is that the concentration of its zeros along the imaginary axis, which is a generalization of the classical results of Selberg.

  • Semiclassical zeta functions for negatively curved manifolds Invited International conference

    Masato TSUJII

    Kyoto Dynamics Days 10  2011.3 

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    Event date: 2011.3

    Language:Others   Presentation type:Oral presentation (general)  

    Venue:京都大学   Country:Japan  

  • 負曲率多様体上の測地流と半古典ゼータ関数 Invited

    Masato TSUJII

    Dynamics of Complex Systems 2011  2011.3 

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    Event date: 2011.3

    Language:Others   Presentation type:Oral presentation (general)  

    Venue:京都大学   Country:Japan  

  • 負曲率多様体上の測地流 Invited

    Masato TSUJII

    談話会  2011.1 

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    Event date: 2011.1

    Language:Others   Presentation type:Oral presentation (general)  

    Venue:東京工業大学   Country:Japan  

  • Functional analytic method in smooth ergodic theory Invited International conference

    Masato TSUJII

    Dynamics and PDE  2010.1 

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    Event date: 2011.1 - 2011.7

    Language:Others   Presentation type:Oral presentation (general)  

    Venue:Mittag-Leffeler Institute   Country:Sweden  

  • 接触アノソフ流と FBI 変換

    Masato TSUJII

    力学系冬の研究集会  2011.1 

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    Event date: 2011.1

    Language:Others   Presentation type:Oral presentation (general)  

    Venue:東京工業大学   Country:Japan  

  • Contact Anosov Flows and the FBI transform Invited International conference

    Masato TSUJII

    Hyperbolic Dynamics in the Sciences  2010.6 

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    Event date: 2010.5 - 2010.6

    Language:Others   Presentation type:Oral presentation (general)  

    Venue:Corinaldo   Country:Italy  

  • On the semi-classical zeta functions for negatively curved manifolds Invited International conference

    Masato TSUJII

    Mini-Workshop: Spectrum of Transfer Operators: Recent Developments and Applications  2009.11 

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    Event date: 2009.11

    Language:Others   Presentation type:Oral presentation (general)  

    Venue:Oberwalfach 数学研究所   Country:Germany  

  • Quasi-compactness of transfer operators for contact Anosov flow Invited International conference

    Masato TSUJII

    WORKSHOP on HYPERBOLIC DYNAMICAL SYSTEMS WITH SINGULARITIES  2009.6 

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    Event date: 2009.6

    Language:Others   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:rwin Schrodinger Institute, Vienna   Country:Austria  

  • Ruelle resonances in contact Anosov flows Invited International conference

    Masato TSUJII

    NCTS 2008 Workshop on Dynamical systems  2008.5 

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    Event date: 2008.5

    Language:Others   Presentation type:Oral presentation (general)  

    Venue:NCTS, Shinchu   Country:Taiwan, Province of China  

  • Quasi-compactness of transfer operators for contact Anosov flows Invited International conference

    Masato TSUJII

    Workshop GREFI-MEFI "From dynamical systems to statistical mechanics  2008.2 

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    Event date: 2008.2 - 2008.3

    Language:Others   Presentation type:Oral presentation (general)  

    Venue:CIRM, Marseille   Country:France  

  • 双曲的な流れにおける相関の減衰と力学系のゼータ関数 Invited

    辻井 正人

    力学系と微分方程式  2007.11 

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    Language:Others   Presentation type:Oral presentation (general)  

    Venue:広島大学理学部   Country:Japan  

  • 力学系のゼータ関数と転移作用素のスペクトル Invited

    辻井 正人

    Encounter with Mathematics  2007.5 

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    Language:Others   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:中央大学   Country:Japan  

  • Virtually expanding dynamics Invited International conference

    Msasato Tsujii

    International workshop on Ergodic theory, Dynamical systems and Climate sciences  2023.3 

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    Event date: 2023.3

    Language:English   Presentation type:Oral presentation (general)  

    Venue:北海道大学   Country:Japan  

  • 力学系のゼータ関数の極の分布について

    辻井 正人

    力学系セミナー  2007.10 

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    Language:Others   Presentation type:Oral presentation (general)  

    Venue:九州大学理学部   Country:Japan  

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MISC

  • Absolutely continuous invariant measures for piecewise real-analytic expanding maps on the plane

    M Tsujii

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   2000.1

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    We prove the existence of absolutely continuous invariant measures for piecewise real-analytic expanding maps on bounded regions in the plane.

  • On continuity of Bowen-Ruelle-Sinai measures in families of one dimensional maps

    M Tsujii

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   1996.3

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    Let us consider a family of maps Q(a)(x) = ax(1 - x) from the unit interval [0, 1] to itself, where a is an element of [0, 4] is the parameter. We show that, for any beta < 2, there exists a subset E There Exists 4 in [0,4] with the properties
    (1) Leb([4 - epsilon,4] - E) < epsilon(beta) for sufficiently small epsilon > 0,
    (2) Q(a) admits an absolutely continuous BRS measure mu(a), when a is an element of E, and
    (3) mu(a) converges to the measure mu(4) as a tends to 4 on the set E.
    Also we give some generalization of this results.

    DOI: 10.1007/BF02102427

  • POSITIVE LYAPUNOV EXPONENTS IN FAMILIES OF ONE-DIMENSIONAL DYNAMIC-SYSTEMS

    M TSUJII

    INVENTIONES MATHEMATICAE   1993.1

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    We give a generalization of Jakobson's theorem [Ja] and a precise estimate for the density of parameters corresponding to systems with absolutely continuous invariant measures.

Professional Memberships

  • Japan Mathematical Society

  • Japan Mathematical Society

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Committee Memberships

  • 日本数学会   出版委員長   Domestic

    2020.4 - 2022.3   

  • 評議員   Councilor   Domestic

    2008.4 - 2009.3   

  • 評議員   九州支部評議員   Domestic

    2008.4 - 2009.3   

Academic Activities

  • Screening of academic papers

    Role(s): Peer review

    2023

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    Type:Peer review 

    Number of peer-reviewed articles in foreign language journals:2

    Number of peer-reviewed articles in Japanese journals:0

  • Screening of academic papers

    Role(s): Peer review

    2019

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    Type:Peer review 

    Number of peer-reviewed articles in foreign language journals:3

    Number of peer-reviewed articles in Japanese journals:0

    Proceedings of International Conference Number of peer-reviewed papers:0

    Proceedings of domestic conference Number of peer-reviewed papers:0

  • Screening of academic papers

    Role(s): Peer review

    2018

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    Type:Peer review 

    Number of peer-reviewed articles in foreign language journals:5

    Number of peer-reviewed articles in Japanese journals:0

    Proceedings of International Conference Number of peer-reviewed papers:0

    Proceedings of domestic conference Number of peer-reviewed papers:0

  • Screening of academic papers

    Role(s): Peer review

    2017

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    Type:Peer review 

    Number of peer-reviewed articles in foreign language journals:3

    Number of peer-reviewed articles in Japanese journals:1

    Proceedings of International Conference Number of peer-reviewed papers:0

    Proceedings of domestic conference Number of peer-reviewed papers:0

  • Screening of academic papers

    Role(s): Peer review

    2016

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    Type:Peer review 

    Number of peer-reviewed articles in foreign language journals:4

    Number of peer-reviewed articles in Japanese journals:0

    Proceedings of International Conference Number of peer-reviewed papers:0

    Proceedings of domestic conference Number of peer-reviewed papers:0

  • Kyushu Journal of mathematics International contribution

    2013.4 - 2014.3

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    Type:Academic society, research group, etc. 

  • その他 International contribution

    Mini-workshop on ergodic theory  ( Japan ) 2008.6

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    Type:Competition, symposium, etc. 

    Number of participants:10

  • その他 International contribution

    Flat surfaces and Teichmuller geodesic flows  ( Japan ) 2008.5

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    Type:Competition, symposium, etc. 

    Number of participants:50

  • Dynamical systems, an international journal International contribution

    2004.4 - Present

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    Type:Academic society, research group, etc. 

  • Ergodic Theory and Dynamical systems International contribution

    2004.4 - Present

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    Type:Academic society, research group, etc. 

  • Nonlinearity International contribution

    2004.4 - 2018.3

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    Type:Academic society, research group, etc. 

  • Dynamical systems, an international journal International contribution

    Role(s): Review, evaluation

    2004.4

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    Type:Peer review 

    researchmap

  • Ergodic Theory and Dynamical systems International contribution

    Role(s): Review, evaluation

    2004.4

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    Type:Peer review 

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Other

  • 典型的なカオス的は流れ(連続力学系)であるアノソフ流における指数的混合性が生成的な条件の下で成立するかとうかは1970年代のアノソフやシナイの研究依頼の懸案であったが,その問題に対し3次元の場合に肯定的な解決を与えた. 結果と証明は論文 "Exponential mixing for generic volume-preserving Anosov flows in dimension three" (プレプリント, arXiv:1601.00063)で発表した.

    2016.6

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    Let M be a closed 3-dimensional Riemann manifold and let 3≤r≤∞. We prove that there exists an open dense subset in the space of Cr volume-preserving Anosov flows on M such that all the flows in it are exponentially mixing.

  • 典型的なカオス的は流れ(連続力学系)であるアノソフ流における指数的混合性が生成的な条件の下で成立するかとうかは1970年代のアノソフやシナイの研究依頼の懸案であったが,その問題に対し3次元の場合に肯定的な解決を与えた. 結果と証明は論文 "Exponential mixing for generic volume-preserving Anosov flows in dimension three" (プレプリント, arXiv:1601.00063)で発表した.

    2016.6

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    Let M be a closed 3-dimensional Riemann manifold and let 3≤r≤∞. We prove that there exists an open dense subset in the space of Cr volume-preserving Anosov flows on M such that all the flows in it are exponentially mixing.

    researchmap

Research Projects

  • Exponential mixing property of Anosov flows and some related topics in quantum chaos

    Grant number:23K20806  2021.4 - 2026.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    辻井 正人

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    Grant type:Scientific research funding

    自然界の諸現象を記述するために、科学では時間経過に伴う変化を「力学系」という数学的対象で表現します。この中には、系自体は単純でも、その振る舞いが複雑で予測不可能になることがあり、「カオス」と呼ばれます。カオスを記述し、解析する方法は、力学系理論において最も重要な課題の1つです。本研究は、特に典型的なカオスの一形態であるアノソフ流に対して理論的で精密な解析を行います。興味深いことに、この研究の中で量子力学との類似性が発見され、多くの研究者の注目を集めています。本研究は、この分野において主導的な役割を果たすことを目指しています。

    CiNii Research

  • アノソフ流の指数混合性と量子カオスの諸問題

    Grant number:21H00994  2021 - 2025

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • 大偏差原理に基づくカオス力学系の構造解析

    Grant number:23K20220  2020.4 - 2025.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    高橋 博樹, 辻井 正人, イェーリッシュ ヨハネス

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    Grant type:Scientific research funding

    一般に「カオス」として知られる非双曲力学系の典型例である2次写像やエノン写像に加えて、数論・幾何学に由来するフックス群作用やタイヒミュラー測地流などの非コンパクト・非双曲力学系の大域構造を大偏差原理により精密に解析する。これに基づき、一般の非コンパクト・非双曲力学系の大偏差原理による理解に向けた理論基盤を構築する。

    CiNii Research

  • 双曲力学系における転送作用素のスペクトルの研究

    Grant number:15H03627  2015 - 2019

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • 測地流の転移作用素と半古典ゼータ関数の研究

    2010 - 2015

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 測地流の転移作用素と半古典ゼータ関数の研究

    Grant number:22340035  2010 - 2014

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • 力学系理論における関数解析的方法の研究

    Grant number:18340044  2006 - 2009

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

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    Authorship:Principal investigator  Grant type:Scientific research funding

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Educational Activities

  • As I have been the dean of Faculty of Mathematics, I am not in charges of lectures. I am supervising 3 master and 2 doctoral course students.

Award for Educational Activities

  • なし

       

Class subject

  • 数学特論13

    2024.10 - 2025.3   Second semester

  • 力学系大意

    2024.10 - 2025.3   Second semester

  • 入門線形代数Ⅱ

    2024.6 - 2024.8   Summer quarter

  • 数学概論Ⅰ・演習

    2024.4 - 2024.9   First semester

  • 入門線形代数Ⅰ

    2024.4 - 2024.6   Spring quarter

  • 卓越基礎講究

    2023.4 - 2024.3   Full year

  • 卓越基礎講究

    2022.4 - 2023.3   Full year

  • MMA講究D

    2021.10 - 2022.3   Second semester

  • 幾何学Ⅰ・演習

    2021.4 - 2021.9   First semester

  • 幾何学1・同演習

    2021.4 - 2021.9   First semester

  • 解析(編入生向け講義)

    2021.4 - 2021.9   First semester

  • 情報解析学演習

    2020.10 - 2021.3   Second semester

  • 情報解析学

    2020.10 - 2021.3   Second semester

  • 幾何学Ⅰ・演習

    2020.4 - 2020.9   First semester

  • 幾何学1・同演習

    2020.4 - 2020.9   First semester

  • 解析(編入生向け講義)

    2020.4 - 2020.9   First semester

  • 数学特論13

    2019.10 - 2020.3   Second semester

  • 力学系大意

    2019.10 - 2020.3   Second semester

  • Dynamical Systems

    2019.10 - 2020.3   Second semester

  • 力学系大意

    2019.10 - 2020.3   Second semester

  • 数学概論VI

    2019.10 - 2020.3   Second semester

  • 数学概論Ⅳ・演習

    2019.10 - 2020.3   Second semester

  • 情報解析学演習

    2019.10 - 2020.3   Second semester

  • 情報解析学

    2019.10 - 2020.3   Second semester

  • 数理科学特論7

    2019.4 - 2019.9   First semester

  • 数理科学特別講義Ⅶ

    2019.4 - 2019.9   First semester

  • 解析(編入生向け講義)

    2019.4 - 2019.9   First semester

  • 力学系大意

    2018.10 - 2019.3   Second semester

  • 数学概論VI

    2018.10 - 2019.3   Second semester

  • 力学系大意

    2018.10 - 2019.3   Second semester

  • 情報解析学演習

    2018.10 - 2019.3   Second semester

  • 情報解析学

    2018.10 - 2019.3   Second semester

  • 数学概論Ⅳ・演習

    2018.10 - 2019.3   Second semester

  • 数学特論13

    2018.10 - 2019.3   Second semester

  • 線形代数学B

    2017.10 - 2018.3   Second semester

  • 線形代数学B

    2017.10 - 2018.3   Second semester

  • 数学基礎2

    2017.10 - 2018.3   Second semester

  • 線形代数学・同演習B

    2017.10 - 2018.3   Second semester

  • 線形代数学・同演習B

    2017.10 - 2018.3   Second semester

  • 数学基礎Ⅱ

    2017.10 - 2018.3   Second semester

  • 線形代数学A

    2017.4 - 2017.9   First semester

  • 線形代数学A

    2017.4 - 2017.9   First semester

  • 線形代数学・同演習A

    2017.4 - 2017.9   First semester

  • 線形代数学・同演習A

    2017.4 - 2017.9   First semester

  • 数学基礎2

    2016.10 - 2017.3   Second semester

  • 微分積分学

    2016.10 - 2017.3   Second semester

  • 微分積分学・同演習II

    2015.10 - 2016.3   Second semester

  • 数理学講究第2

    2015.4 - 2016.3   Full year

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    2015.4 - 2015.9   First semester

  • 微分積分学・同演習I

    2015.4 - 2015.9   First semester

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    2014.10 - 2015.3   Second semester

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    2014.4 - 2015.3   Full year

  • 位相(基礎数学3)

    2014.4 - 2014.9   First semester

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    2013.10 - 2014.3   Second semester

  • 数学特論13

    2013.10 - 2014.3   Second semester

  • 数学II

    2013.10 - 2014.3   Second semester

  • 力学系大意

    2013.10 - 2014.3   Second semester

  • 数学概論1

    2013.10 - 2014.3   Second semester

  • 数学2B

    2013.4 - 2013.9   First semester

  • 数学2B

    2013.4 - 2013.9   First semester

  • 微分積分学・同演習B

    2012.10 - 2013.3   Second semester

  • 微分積分学・同演習B

    2012.10 - 2013.3   Second semester

  • 線形代数学

    2012.4 - 2012.9   First semester

  • 微分積分学

    2012.4 - 2012.9   First semester

  • 数学2B

    2012.4 - 2012.9   First semester

  • 数学2B

    2012.4 - 2012.9   First semester

  • 微分積分学・同演習A

    2012.4 - 2012.9   First semester

  • 線形代数学・同演習B

    2011.10 - 2012.3   Second semester

  • 微分積分学・同演習B

    2011.10 - 2012.3   Second semester

  • 線形代数学・同演習A

    2011.4 - 2011.9   First semester

  • 微分積分学・同演習A

    2011.4 - 2011.9   First semester

  • 数学2B

    2011.4 - 2011.9   First semester

  • 数学2B

    2011.4 - 2011.9   First semester

  • 微分積分学・同演習A

    2010.10 - 2011.3   Second semester

  • 微分積分学・同演習A

    2010.10 - 2011.3   Second semester

  • 微分積分学・同演習A

    2010.10 - 2011.3   Second semester

  • 微分積分学・同演習A

    2010.4 - 2010.9   First semester

  • 数学2B

    2010.4 - 2010.9   First semester

  • 数学2B

    2010.4 - 2010.9   First semester

  • 微分積分学・同演習A

    2010.4 - 2010.9   First semester

  • 微分積分学・同演習A

    2010.4 - 2010.9   First semester

  • 微分積分学

    2009.4 - 2009.9   First semester

  • 線形代数・同演習A

    2009.4 - 2009.9   First semester

  • 数学2B

    2009.4 - 2009.9   First semester

  • 数学2B

    2009.4 - 2009.9   First semester

  • 解析学B1・同演習

    2009.4 - 2009.9   First semester

  • 情報解析学・同演習

    2008.10 - 2009.3   Second semester

  • 解析学A1・同演習

    2008.10 - 2009.3   Second semester

  • 力学系大意

    2008.10 - 2009.3   Second semester

  • 数学特論13(力学系)

    2008.10 - 2009.3   Second semester

  • 数学2B

    2008.4 - 2008.9   First semester

  • 数学2B

    2008.4 - 2008.9   First semester

  • 力学系大意

    2007.10 - 2008.3   Second semester

  • 数学特論13

    2007.10 - 2008.3   Second semester

  • 微分積分続論

    2007.4 - 2007.9   First semester

  • 線形代数・同演習A

    2007.4 - 2007.9   First semester

  • 線形代数・同演習A

    2007.4 - 2007.9   First semester

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FD Participation

  • 2023.8   Role:Planning   Title:数理学府教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2022.7   Role:Participation   Title:数理学府教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2022.4   Role:Participation   Title:数理学府FD

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2021.9   Role:Participation   Title:JST 次世代研究者挑戦的研究プログラム 説明会

    Organizer:University-wide

  • 2021.7   Role:Participation   Title:数理学府FD

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2021.3   Role:Speech   Title:数理学府FD

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2021.3   Role:Speech   Title:数理学府FD

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2021.2   Role:Speech   Title:数理学府教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2020.3   Role:Moderator   Title:教員会議 on Zoom

    Organizer:Undergraduate school department

  • 2019.12   Role:Participation   Title:教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2019.4   Role:Participation   Title:教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2018.4   Role:Speech   Title:教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2018.3   Role:Participation   Title:教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2015.12   Role:Participation   Title:教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2015.7   Role:Participation   Title:教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2014.12   Role:Moderator   Title:(数理学府)教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2014.7   Role:Moderator   Title:(数理学府)教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2014.7   Role:Participation   Title:(数理学府)教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2012.5   Role:Participation   Title:数理学府教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2011.5   Role:Participation   Title:数理学府教員会議

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2010.3   Role:Participation   Title:シンポジウム:数学力低下にどう対処するか ー高等学校・大学・教員採用の現場からー

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2008.3   Role:Participation   Title:数理学府教員会議

    Organizer:University-wide

  • 2007.4   Role:Participation   Title:第1回全学FD

    Organizer:University-wide

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Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.

  • 2015  筑波大学理工学群数学  Classification:Intensive course  Domestic/International Classification:Japan 

    Semester, Day Time or Duration:後期

  • 2014  北海道大学理学部  Classification:Intensive course  Domestic/International Classification:Japan 

    Semester, Day Time or Duration:前期

  • 2014  大阪大学理学部  Classification:Intensive course  Domestic/International Classification:Japan 

    Semester, Day Time or Duration:前期

Participation in international educational events, etc.

  • 2021.3

    Bernouilli center

    “3-dimensional Anosov flows”, 2021年3月26日〜30日 Spring School on Transfer operators (Classical and Modern Techniques), CIB, Lausanne, Switzerland

      More details

    Venue:Lausanne, Swiss

    Number of participants:200

  • 2019.12

    CIRM

    Thermodynamic Formalism: Applications to Probability, Geometry and Fractals

      More details

    Venue:France, Marseille

    Number of participants:60

  • 2018.5

    ICTP (International center of theoretical physics)

    TMU-ICTP school and conference on dynamical systems and ergodic theory I

      More details

    Venue:Iran, Tehran

    Number of participants:100

Other educational activity and Special note

  • 2013  Class Teacher  全学

  • 2012  Class Teacher  全学

  • 2010  Class Teacher  全学

Outline of Social Contribution and International Cooperation activities

  • I attended as a lecturer to TMU-ICTP School and Conference on Dynamical Systems and Ergodic Theory at Tarbiat Modares University.

Social Activities

  • 高大接続,特に,新しい入試制度に関する研究の一環として,高校生向けに数学の講義をおこなった.また,高校生の研究発表について補助と発表の評価について関わった.

    東筑高校  2017.6

     More details

    Audience:Infants, Schoolchildren, Junior students, High school students

    Type:Seminar, workshop

  • 高大接続,特に,新しい入試制度に関する研究の一環として,高校生向けに数学の講義をおこなった.また,高校生の研究発表について補助と発表の評価について関わった.

    東筑高校  2017.6

     More details

    Type:Seminar, workshop

    researchmap

  • 過去3年間に引き続きエクセレント・スチューデント・イン・サイエンス事業の数学担当をした.

    九州大学理学部  数理学研究教育棟,九州大学理学部大会議室他  2013.4

     More details

    Audience:General, Scientific, Company, Civic organization, Governmental agency

    Type:Seminar, workshop

    エクセレント・スチューデント・イン・サイエンス事業は科学技術振興機構と九州大学が行っている意欲・能力ある高校生を次世代の科学者に育てるための取り組みである.この講座において数学部門の担当をして,半年間におよび月二回のセミナーを行った.

  • 過去3年間に引き続きエクセレント・スチューデント・イン・サイエンス事業の数学担当をした.

    九州大学理学部  数理学研究教育棟,九州大学理学部大会議室他  2013.4

     More details

    Type:Seminar, workshop

    エクセレント・スチューデント・イン・サイエンス事業は科学技術振興機構と九州大学が行っている意欲・能力ある高校生を次世代の科学者に育てるための取り組みである.この講座において数学部門の担当をして,半年間におよび月二回のセミナーを行った.

    researchmap

  • 理学部の社会貢献委員として出張講義の手配を行った.また,自身でいくつかの高校の出張講義に出向いた.

    福岡県立八女高校,佐賀県立武雄高校 他  2012.9

     More details

    Audience:Infants, Schoolchildren, Junior students, High school students

    Type:Seminar, workshop

  • 理学部の社会貢献委員として出張講義の手配を行った.また,自身でいくつかの高校の出張講義に出向いた.

    福岡県立八女高校,佐賀県立武雄高校 他  2012.9

     More details

    Type:Seminar, workshop

    researchmap

  • 過去2年間に引き続きエクセレント・スチューデント・イン・サイエンス事業の数学担当をした.

    九州大学理学部  数理学研究教育棟,九州大学理学部大会議室他  2012.4

     More details

    Audience:General, Scientific, Company, Civic organization, Governmental agency

    Type:Seminar, workshop

    エクセレント・スチューデント・イン・サイエンス事業は科学技術振興機構と九州大学が行っている意欲・能力ある高校生を次世代の科学者に育てるための取り組みである.この講座において数学部門の担当をして,半年間におよび月二回のセミナーを行った.

  • 過去2年間に引き続きエクセレント・スチューデント・イン・サイエンス事業の数学担当をした.

    九州大学理学部  数理学研究教育棟,九州大学理学部大会議室他  2012.4

     More details

    Type:Seminar, workshop

    エクセレント・スチューデント・イン・サイエンス事業は科学技術振興機構と九州大学が行っている意欲・能力ある高校生を次世代の科学者に育てるための取り組みである.この講座において数学部門の担当をして,半年間におよび月二回のセミナーを行った.

    researchmap

  • 現代数学入門「微分方程式で見る世界」 微分方程式を使って現象を記述することについて入門的な講義をした.

    九州大学大学院数理学研究院 ・ 福岡県教育委員会  九州大学理学部大会議室  2007.8

     More details

    Audience:General, Scientific, Company, Civic organization, Governmental agency

    Type:Lecture

  • 現代数学入門「微分方程式で見る世界」 微分方程式を使って現象を記述することについて入門的な講義をした.

    九州大学大学院数理学研究院 ・ 福岡県教育委員会  九州大学理学部大会議室  2007.8

     More details

    Type:Visiting lecture

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Activities contributing to policy formation, academic promotion, etc.

  • 2018.5   ICTP(International center for theoretical physics)

    UNESCOの機関である国際理論物理学研究所(トリエステ,イタリア)は発展途上国における数学の国際的な研究集会とそれに伴う大学院生の教育のプログラムを推進している.当該の研究集会は本年はテヘラン(イラン)で行われ,知人の関係者から講演を依頼されたので参加した.

Acceptance of Foreign Researchers, etc.

  • IAS, Princeton, USA

    Acceptance period: 2019.5   (Period):Less than 2 weeks

    Nationality:China

    Business entity:Japan Society for the Promotion of Science

  • Armenian Academy of Science

    Acceptance period: 2018.9 - 2018.12   (Period):1 month or more

    Nationality:Armenia

    Business entity:Japan Society for the Promotion of Science

  • PUC Rio

    Acceptance period: 2008.10   (Period):Less than 2 weeks

    Nationality:Spain

    Business entity:Japan Society for the Promotion of Science

  • Rice University

    Acceptance period: 2008.6   (Period):Less than 2 weeks

    Nationality:Russian Federation

    Business entity:Other

  • Univ. Renne

    Acceptance period: 2008.5   (Period):Less than 2 weeks

    Nationality:Russian Federation

    Business entity:Science and Technology Agency

Travel Abroad

  • 2014.8

    Staying countory name 1:Korea, Republic of   Staying institution name 1:Chungnam 大学(韓国 大田)

    Staying institution name 2:Coex

  • 2010.5

    Staying countory name 1:Italy   Staying institution name 1:Corinaldo

  • 2010.1 - 2010.2

    Staying countory name 1:Sweden   Staying institution name 1:Mittag Leffeler Institute

  • 2009.12

    Staying countory name 1:Sweden   Staying institution name 1:KTH

  • 2009.9 - 2009.11

    Staying countory name 1:France   Staying institution name 1:Fourier Institute

    Staying countory name 2:Italy   Staying institution name 2:Rome university 3

    Staying countory name 3:Germany   Staying institution name 3:Ecole Normal

    Staying institution name (Other):MFO

  • 2009.3 - 2009.4

    Staying countory name 1:United States   Staying institution name 1:Rice University

  • 2008.5

    Staying countory name 1:Taiwan, Province of China   Staying institution name 1:NCTS(国家理論科学中心),

  • 2008.2

    Staying countory name 1:France   Staying institution name 1:CIRM, Luminy

  • 2007.6

    Staying countory name 1:China   Staying institution name 1:中国科学院

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