Kyushu University Academic Staff Educational and Research Activities Database
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Yutaka ISHII Last modified date:2020.01.30

Professor / Department of Mathematics
Department of Mathematical Sciences
Faculty of Mathematics

Graduate School
Undergraduate School

Academic Degree
Ph D (Mathematical Sciences), University of Tokyo, March 1998
Country of degree conferring institution (Overseas)
Field of Specialization
dynamical systems
Total Priod of education and research career in the foreign country
Outline Activities
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.
Research Interests
  • Combinatorial study of complex Henon maps
    keyword : Henon maps, complex dynamics, Julia sets, hyperbolicity, parameter loci
Academic Activities
1. Zin ARAI, Yutaka ISHII, On parameter loci of the H'enon family., Commun. Math. Phys., 2018.12.
2. Yutaka ISHII, Dynamics of polynomial diffeomorphisms of C^2: Combinatorial and topological aspects., Arnold Math. J., 2017.01, The purpose of this paper is to survey some results, questions and problems on the dynamics of polynomial diffeomorphisms of C^2 including complex Henon maps with an emphasis on the combinatorial and topological aspects of their Julia sets..
3. Yutaka ISHII, Hyperbolic polynomial diffeomorphisms of C^2. III: Iterated monodromy groups., Advances in Mathematics, 255, 242-304, 2014.01.
4. Yutaka Ishii, John Smillie, Homotopy shadowing., Amer. J. Math. , 132, 4, 987-1029, 2010.12, Michael Shub proved in 1969 that the topological conjugacy class of an expanding endomorphism on a compact manifold is determined by its homotopy type. In this article we generalize this result in two directions. In one direction we consider certain expanding maps on metric spaces. In a second direction we consider maps which are hyperbolic with respect to product cone fields on a product manifold. A key step in the proof is to establish a shadowing theorem for pseudo-orbits with some additional homotopy information..
Educational Activities
I taught calculus to freshmen and introduction to complex dynamics to 4th grade undergraduate and graduate students in math department.