ISHII YUTAKA
Organization
Faculty of Mathematics Division of Analysis Professor
School of Sciences Department of Mathematics（Joint Appointment）
Graduate School of Mathematics Department of Mathematics（Joint Appointment）
Joint Graduate School of Mathematics for Innovation
（Joint Appointment）
Title
Professor
Contact information
Profile
The main theme of my research is a combinatorial study of complex dynamical systems in dimension two, namely the complex Henon maps. I am now working on a criterion of their hyperbolicity, topology and combinatorics of their Julia sets and of their parameter loci, and applications of such complex methods to real dynamics.
I gave a series of lectures on the dynamics of complex Henon maps both in Tokyo Institute of Technology and in Hokkaido University, on symbolic dynamics and data storage in Tokushima University.
I gave a public lecture under the title "Dimension, Fractals and Dynamical Systems" organized by the Department of Mathematics, Kyushu University.
External link
Degree
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Ph D (Mathematical Sciences), University of Tokyo, March 1998
Research Interests・Research Keywords
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Research theme：Visualization of 4D spaces with VR
Keyword：higher-dimensional spaces, virtual reality, Julia sets
Research period： 2018.4
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Research theme：高次元ラップ数公式とエントロピーの誤差評価付き計算
Keyword：ラップ数公式、エントロピー、区間演算
Research period： 1998.1
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Research theme：量子トンネル効果と高次元複素力学系
Keyword：トンネル効果、Julia 集合、Laputa 鎖
Research period： 1998.1
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Research theme：Combinatorial study of complex Henon maps
Keyword：Henon maps, complex dynamics, Julia sets, hyperbolicity, parameter loci
Research period： 1997.10
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Research theme：Lozi 写像に対する kneading 理論
Keyword：Lozi 写像、二ーディング理論、エントロピー、単調性
Research period： 1992.4
Papers
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Polyvision 4D space manipulation through multiple projections International journal
Keigo Matsumoto, Nami Ogawa, Hiroyuki Inou, Shizuo Kaji, Yutaka Ishii, Michitaka Hirose
SIGGRAPH Asia 2019 Emerging Technologies - International Conference on Computer Graphics and Interactive Techniques, SA 2019 SIGGRAPH Asia 2019 Emerging Technologies, SA 2019 36 - 37 2019.11
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On parameter loci of the H'enon family. Invited Reviewed International journal
Zin ARAI, Yutaka ISHII
Commun. Math. Phys. 2018.12
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Dynamics of polynomial diffeomorphisms of C^2: Combinatorial and topological aspects. Invited Reviewed International journal
Yutaka ISHII
Arnold Math. J. 2017.1
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Hyperbolic polynomial diffeomorphisms of C^2. III: Iterated monodromy groups. Reviewed International journal
Yutaka ISHII
Advances in Mathematics 255 242 - 304 2014.1
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Homotopy shadowing. Reviewed International journal
Yutaka Ishii, John Smillie
Amer. J. Math. 132 ( 4 ) 2010.12
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On the Hausdorff dimension of the recurrent sets induced from endomorphisms of free groups. Reviewed International journal
Yutaka Ishii, Tatsuya Oka
J. Fractal Geom. 9 ( 1 ) 171 - 192 2023.4
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複素力学系の諸問題 Invited International journal
石井豊
数理解析研究所講究録 2211 2022.4
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M_4 is regular-closed. Invited Reviewed International journal
Yutaka ISHII, Yutaro HIMEKI
Ergod. Th. & Dynam. Sys. 2020.1
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Boundary of the horseshoe locus for the H'enon family Reviewed International journal
Zin Arai, Yutaka Ishii, Hiroki Takahasi
SIAM J. Appl. Dyn. Syst. 17 ( 3 ) 2234 - 2248 2018.4
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Corrigendum to ``Hyperbolic polynomial diffeomorphisms of C^2. II: Hubbard trees.'' Reviewed International journal
Yutaka Ishii
Advances in Mathematics 226 ( 4 ) 2011.7
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Julia sets and chaotic tunneling I. Reviewed International journal
Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda
J. Phys. A: Math. Theor. 42 2009.6
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Julia sets and chaotic tunneling II. Reviewed International journal
Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda
J. Phys. A: Math. Theor. 42 2009.6
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Hyperbolic polynomial diffeomorphisms of C^2. II: Hubbard trees. Reviewed International journal
Yutaka Ishii
Advances in Mathematics 220 ( 4 ) 2009.5
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Hyperbolic polynomial diffeomorphisms of C^2. I: A non-planar map. Reviewed International journal
Yutaka Ishii
Advances in Mathematics 218 ( 2 ) 2008.4
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Chaos attracts tunneling trajectories: A universal mechanism of chaotic tunneling. Reviewed International journal
Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda
Europhysics Letters 2008.1
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Lap number entropy formula for piecewise affine and projective maps. Reviewed International journal
Yutaka Ishii, Duncan Sands
Nonlinearity 2007.1
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Note on a paper by Kawasaki and Sasa on Bernoulli coupled map lattices. Reviewed International journal
Yutaka Ishii
Journal of Physics A: Mathematical and General 2006.1
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Julia set describes quantum tunnelling in the presence of chaos. Reviewed International journal
Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda
Journal of Physics A: Mathematical and General 35 ( 17 ) L225 - L231 2002.1
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Monotonicity of the Lozi family near the tent-maps. Reviewed International journal
Yutaka Ishii, Duncan Sands
Communications in Mathematical Physics 1998.1
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Towards a kneading theory for Lozi mappings. II: Monotonicity of the topological entropy and Hausdorff dimension of attractors. Reviewed International journal
Yutaka Ishii
Communications in Mathematical Physics 1997.1
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Towards a kneading theory for Lozi mappings I: A solution of the pruning front conjecture and the first tangency problem. Reviewed International journal
Yutaka Ishii
Nonlinearity 1997.1
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Ising models, Julia sets, and similarity of the maximal entropy measures. Reviewed International journal
Yutaka Ishii
J.Statist.Phys. 1995.1
Books
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カオス力学系入門 第2版
国府 寛司・石井 豊・新居 俊作・木坂 正史（ Role： Joint translator）
共立出版 2003.11
Presentations
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Information theory and symbolic dynamics Invited
Y.Ishii
TIN workshop 2009.7
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Hyperbolic polynomial diffeomorphisms of $C^2$. Invited International conference
Y.Ishii
Dynamique conforme, geometrie hyperbolique, et fractions continues 2005.6
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Hyperbolic polynomial diffeomorphisms of $C^2$. Invited International conference
Y.Ishii
Hayama Symposium on Several Complex Variables 2004.12
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Global monotonicity conjecture and renormalization for the skew-Lozi family. Invited International conference
Y.Ishii
Semi-annual conference on dynamical systems 1999.10
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Global monotonicity conjecture and renormalization for the skew-Lozi family. Invited International conference
Y.Ishii
Dynamics and geometry seminar 1999.11
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Global monotonicity conjecture and renormalization for the skew-Lozi family. Invited International conference
Y.Ishii
Dynamics seminar 2000.4
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On the hyperbolicity of some complex H?'enon maps. Invited International conference
Y.Ishii
Hayama Symposium on Several Complex Variables 2000.12
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Sur l'hyperbolicit?'e de quelques applications de H?'enon complexes. Invited International conference
Y.Ishii
Seminaire de dynamique 2001.3
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A lap number formula in higher dimensions and rigorous entropy estimates for Lozi maps. Invited International conference
Y.Ishii
New Directions in Dynamical Systems 2002.8
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A lap number formula in higher dimensions and rigorous entropy estimates for Lozi maps. Invited International conference
Y.Ishii
Ergodic Theory Workshop 2002.12
MISC
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バーチャル・リアリティを用いた 4 次元可視化プロジェクト
石井豊
数学通信 2022.4
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数学と出会ったころ: 思い出の紙一枚
石井豊
数学セミナー 2004.12
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高次元複素力学系と「和田の湖」
石井豊
数学セミナー 2004.11
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離散可積分系と離散力学系 ---不変量の視点から---
石井豊
数理科学 2003.9
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物理現象と複素力学系
石井豊
数理科学 1999.10
Professional Memberships
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日本数学会
Academic Activities
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Screening of academic papers
Role(s)： Peer review
2017
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organizing committee International contribution
International symposium on complexified dynamics, tunnelling and chaos （ Ritsumeikan University Japan ） 2005.8 - Present
Research Projects
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「かたち」と「うごき」を表す高次元データ記述子の開発
Grant number：22H05107 2022 - 2026
日本学術振興会・文部科学省 科学研究費助成事業 学術変革領域研究(A)
Authorship：Coinvestigator(s) Grant type：Scientific research funding
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複素２次元力学系における相空間とパラメータ空間の新たな対応関係の構築
Grant number：20H01809 2020 - 2024
日本学術振興会 科学研究費助成事業 基盤研究(B)
Authorship：Principal investigator Grant type：Scientific research funding
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非一様双曲的な実および複素Henon写像の力学系
2019 - 2020
日本学術振興会 二国間交流
Authorship：Principal investigator Grant type：Joint research
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VR を用いた４次元空間の可視化と複素力学系
Grant number：18K18722 2018 - 2020
日本学術振興会 科学研究費助成事業 挑戦的研究（萌芽）
Authorship：Principal investigator Grant type：Scientific research funding
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複素エノン写像の力学系:相空間からパラメータ空間へ
Grant number：25287020 2013 - 2018
日本学術振興会 科学研究費助成事業 基盤研究(B)
Authorship：Principal investigator Grant type：Scientific research funding
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複素2変数力学系の実3次元可視化について
Grant number：25610020 2013 - 2016
科学研究費助成事業 挑戦的萌芽研究
Authorship：Principal investigator Grant type：Scientific research funding
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複素Ｈｅｎｏｎ写像族のパラメータ空間の力学系的研究
Grant number：21740125 2009 - 2012
科学研究費助成事業 若手研究(B)
Authorship：Principal investigator Grant type：Scientific research funding
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体積保存系としてのＫ３曲面上の複素力学系
Grant number：18740091 2006 - 2008
科学研究費助成事業 若手研究(B)
Authorship：Principal investigator Grant type：Scientific research funding
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二次元複素力学系のコンビナトリアルな研究
Grant number：14740120 2002 - 2004
科学研究費助成事業 若手研究(B)
Authorship：Principal investigator Grant type：Scientific research funding
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複素 Henon 写像のコンビナトリアルな研究 International coauthorship
1999.10
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Lozi 写像の単調性とラップ数公式 International coauthorship
1995.6
Educational Activities
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I taught calculus and linear algebra to freshmen and introduction to metric space topology to undergraduate students in math department.
Class subject
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微分積分学Ⅱ
2023.10 - 2024.3 Second semester
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力学系大意
2023.10 - 2024.3 Second semester
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微分積分学Ⅰ
2023.4 - 2023.9 First semester
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数学概論Ⅱ・演習
2023.4 - 2023.9 First semester
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微分積分学Ⅱ
2021.10 - 2022.3 Second semester
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微分積分学Ⅰ
2021.4 - 2021.9 First semester
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コアセミナーⅠ
2021.4 - 2021.9 First semester
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数学概論Ⅱ・演習
2021.4 - 2021.9 First semester
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線形代数学・同演習Ｂ
2020.10 - 2021.3 Second semester
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微分積分学
2020.10 - 2021.3 Second semester
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数学概論Ⅱ・演習
2020.4 - 2020.9 First semester
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線形代数学・同演習Ａ
2020.4 - 2020.9 First semester
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線形代数
2020.4 - 2020.9 First semester
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微分積分学
2019.10 - 2020.3 Second semester
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線形代数学・同演習Ｂ
2019.10 - 2020.3 Second semester
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線形代数
2019.4 - 2019.9 First semester
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線形代数学・同演習Ａ
2019.4 - 2019.9 First semester
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数学概論Ⅱ・演習
2019.4 - 2019.9 First semester
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線形代数学・同演習Ｂ
2018.10 - 2019.3 Second semester
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線形代数学・同演習Ｂ
2018.10 - 2019.3 Second semester
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微分積分学
2018.10 - 2019.3 Second semester
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線形代数学・同演習Ａ
2018.4 - 2018.9 First semester
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線形代数学・同演習Ａ
2018.4 - 2018.9 First semester
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線形代数学Ｂ
2017.10 - 2018.3 Second semester
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線形代数学Ａ
2017.4 - 2017.9 First semester
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線形代数学Ｂ
2016.10 - 2017.3 Second semester
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線形代数学Ａ
2016.4 - 2016.9 First semester
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線形代数学Ｂ
2015.10 - 2016.3 Second semester
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線形代数学Ａ
2015.4 - 2015.9 First semester
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微分積分学
2014.4 - 2015.3 Full year
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数学演習 I
2014.4 - 2014.9 First semester
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複素解析学大意
2014.4 - 2014.9 First semester
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数学概論４・演習
2012.10 - 2013.3 Second semester
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力学系大意
2012.10 - 2013.3 Second semester
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数学概論２・演習
2012.4 - 2012.9 First semester
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基礎数学演習
2011.4 - 2012.3 Full year
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数学入門演習
2011.4 - 2011.9 First semester
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数学概論２
2011.4 - 2011.9 First semester
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Google と線形代数
2011.4 - 2011.9 First semester
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数学概論１・演習
2008.10 - 2009.3 Second semester
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数学概論１・演習
2007.10 - 2008.3 Second semester
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数学概論１・演習
2006.10 - 2007.3 Second semester
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数学基礎演習Ⅱ
2005.10 - 2006.3 Second semester
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複素解析学大意
2004.10 - 2005.3 Second semester
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数学特論11,12
2004.10 - 2005.3 Second semester
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数学基礎演習Ⅱ
2004.10 - 2005.3 Second semester
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解析学B2
2003.4 - 2003.9 First semester
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ルベーグ積分論演習・関数論演習
2003.4 - 2003.9 First semester
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解析学B1
2003.4 - 2003.9 First semester
FD Participation
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2022.4 Role：Moderator Title：数理学府FD
Organizer：[Undergraduate school/graduate school/graduate faculty]
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2021.7 Role：Participation Title：数理学府FD
Organizer：[Undergraduate school/graduate school/graduate faculty]
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2021.3 Role：Participation Title：数理学府FD
Organizer：[Undergraduate school/graduate school/graduate faculty]
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2004.4 Role：Participation Title：不明
Organizer：University-wide
Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.
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2014 名古屋大学多元数理学研究科 Classification:Intensive course Domestic/International Classification:Japan
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2008 京都大学情報学研究科 Classification:Intensive course Domestic/International Classification:Japan
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2006 Departement de Mathenatiques, Universite de Rennes, France Classification:Affiliate faculty Domestic/International Classification:Overseas
Semester, Day Time or Duration：2006.6
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2005 北海道大学理学部 Classification:Intensive course Domestic/International Classification:Japan
Semester, Day Time or Duration：2005 年度後期
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2005 東京工業大学大学院理工学研究科 Classification:Intensive course Domestic/International Classification:Japan
Semester, Day Time or Duration：2005 年度前期
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2002 Departement de Mathematiques, Universite de Paris-Sud, France Classification:Affiliate faculty Domestic/International Classification:Overseas
Semester, Day Time or Duration：2002.3 -- 2002.4
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2002 徳島大学総合科学部 Classification:Intensive course Domestic/International Classification:Japan
Semester, Day Time or Duration：2002.9
Outline of Social Contribution and International Cooperation activities
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無し
Social Activities
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「次元・フラクタル・力学系」 一般市民を対象とした講演
九州大学数理学研究院 九州大学 2005.8
Acceptance of Foreign Researchers, etc.
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数理学研究院
Acceptance period： 2023.1 - 2026.7 （Period）：1 month or more
Nationality：United Kingdom
Business entity：Japan Society for the Promotion of Science
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Centrum voor Wiskunde en Informatica
Acceptance period： 2005.3 （Period）：Less than 2 weeks
Nationality：Netherlands
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CNRS, Universite de Paris VII
Acceptance period： 2003.7 （Period）：Less than 2 weeks
Nationality：France
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Cornell University & Universite de Provence
Acceptance period： 2001.1 （Period）：Less than 2 weeks
Nationality：United States
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Kyoto University
Acceptance period： 1998.1 （Period）：Less than 2 weeks
Nationality：France
Travel Abroad
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2010.3 - 2011.3
Staying countory name 1：France Staying institution name 1：Centre de Mathematiques Laurent Schwartz, Ecole Polytechnique
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2006.6
Staying countory name 1：France Staying institution name 1：Departement de Mathematiques, Universite de Rennes
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2004.1 - 2004.2
Staying countory name 1：France Staying institution name 1：Institut Henri Poincare
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2003.9 - 2003.12
Staying countory name 1：Japan Staying institution name 1：RIMS, Kyoto University
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2002.3 - 2002.4
Staying countory name 1：France Staying institution name 1：Departement de Mathematiques, Universite de Paris-Sud
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2001.3 - 2001.4
Staying countory name 1：France Staying institution name 1：Departement de Mathematiques, Universite de Paris-Sud
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1999.10 - 2000.9
Staying countory name 1：United States Staying institution name 1：Department of Mathematics, Cornell University
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1997.11 - 1997.12
Staying countory name 1：United States Staying institution name 1：Institute for Mathematical Sciences, State University of New York at Stony Brook
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1994.7 - 1996.8
Staying countory name 1：France Staying institution name 1：Departement de Mathematiques, Universite de Paris-Sud