Yutaka ISHII
associate professor
Department of Mathematics, Kyushu University
Motooka, Fukuoka 819-0395, Japan
Curriculum Vitae†
Name: Yutaka ISHII
Date of Birth: March 4, 1970
Place of Birth: Yokohama, Japan
Civil status: married, two children
Nationality: Japanese
Languages: Japanese > English > French
Academic degrees†
- Eiko High School, graduated in March 1988.
- B. Sc., "mainly in mathematics'', Kyoto University, March 1992.
- M. Sc., mathematics, Kyoto University, March 1994.
- Ph. D., mathematical sciences, University of Tokyo, March 1998.
Ph.D. thesis†
- Title: A kneading theory for Lozi mappings.
- Advisor: Professor Mitsuhiro Shishikura (currently at Kyoto University)
Positions held†
- Associate professor, Department of Mathematics, Kyushu University, September 2003 - to date.
- Research associate, Department of Mathematics, Kyushu University, January 1998 - August 2003.
- Maitre de conference (mois d'invit'e), Universit'e de Paris XI (Orsay), France, March 2002 - April 2002.
- JSPS research fellow (DC1), University of Tokyo, April 1994 - March 1997.
Series of lectures†
- "Data storage and symbolic dynamics'', at Tokushima University (2002)
- "Dynamics of complex H'enon maps'', at Tokyo Institute of Technology (2005).
- "Dynamics of complex H'enon maps'', at Hokkaido University (2005).
- "Data storage and symbolic dynamics'', at Kyoto University (2008).
Research visits (long term and invited)†
- Universit'e de Paris XI (Orsay), France, July 1994 - August 1996, visiting researcher.
- IMS, SUNY at Stony Brook, USA, November 1997 - December 1997, invited researcher.
- Cornell University, USA, October 1999 - September 2000, invited researcher.
- Universite de Paris XI (Orsay), France, March 2001, visitor.
- Cornell University, USA, September 2001, visitor.
- Universit'e de Paris XI (Orsay), France, March 2002 - April 2002, maitre de conference.
- RIMS, Kyoto University, Japan, September 2003 - December 2003, long-term visitor.
- Institut Henri Poincar'e, France, January 2004 - February 2004, visitor.
- Scuola Normale Superiore di Pisa, Italy, November 2005.
- Universit'e de Rennes, France, May 2006.
- Ecole Polytechnique, France, March 2010 - March 2011.
Visitors†
- Vincent Naudot (Kyoto University, Japan), 1998.
- Duncan Sands (State University of New York at Stony Brook, USA), July 1998.
- John H. Hubbard (Cornell University, USA and Universit'e de Provence, France), May 2001.
- Charles Favre (CNRS and Universit'e de Paris VII, France), July 2003.
- Pieter Collins (CWI, The Netherlands), February 2005.
- Anton Zorich (Universit'e de Rennes, France), May 2008.
Research areas†
Dynamical systems (in particular, low-dimensional dynamics, symbolic dynamics, and complex dynamics).
Key words†
Lozi map, kneading theory, pruning front, lap number entropy formula, monotonicity of entropy, boundary of chaos, real and complex H'enon map, Julia set, hyperbolicity, Hubbard tree, horseshoe locus.
Publications and Preprints†
Henon maps, polynomial diffeomorphisms of C^2†
- Hyperbolic polynomial diffeomorphisms of C^2. I: A non-planar map.
Adv. Math. 218, no. 2, pp. 417-464 (2008).
- Hyperbolic polynomial diffeomorphisms of C^2. II: Hubbard trees.
Adv. Math. 220, no. 4, pp. 985-1022 (2009).
Corrigendum: Adv. Math. 226, no. 4, pp. 3850-3855 (2011).
- Homotopy shadowing. (with J. Smillie)
Amer. J. Math. 132, no. 4, pp. 987-1029 (2010).
- Hyperbolic polynomial diffeomorphisms of C^2. III: Iterated monodromy groups.
In preparation (2011).
- On the parameter loci of the Henon family. (with Z. Arai)
In preparation (2011).
Lozi maps, piecewise affine/projective maps†
- Towards a kneading theory for Lozi mappings I: A solution of the pruning front conjecture and the first tangency problem.
Nonlinearity 10, no. 3, pp. 731-747 (1997).
- Towards a kneading theory for Lozi mappings II: Monotonicity of the topological entropy and Hausdorff dimension of attractors.
Commun. Math. Phys. 190, no. 2, pp. 375-394 (1997).
- Monotonicity of the Lozi family near the tent-maps. (with D. Sands)
Commun. Math. Phys. 198, no. 2, pp. 397-406 (1998).
- Lap number entropy formula for piecewise affine and projective maps in several dimensions. (with D. Sands)
Nonlinearity 20, no. 12, 2755-2772 (2007).
Corrigendum: Nonlinearity 21, no. 6, pp. 1411-1411 (2008).
- On some conjectures concerning the entropy of Lozi maps. (with D. Sands)
In preparation (2011).
Physics-related papers and others†
- Quantum tunneling phenomena and complex dynamics.
Unpublished manuscript (1999).
- Julia set describes quantum tunnelling in the presence of chaos. (with A. Shudo and K. S. Ikeda)
J. Phys. A: Math. Gen. 35, no. 17, L225-L231 (2002).
- Note on a paper by Kawasaki and Sasa on Bernoulli coupled map lattices.
J. Phys. A: Math. Gen. 39, no. 45, 14043-14046 (2006).
- Chaos attracts tunneling trajectories: A universal mechanism of chaotic tunneling. (with A. Shudo and K. S. Ikeda)
Europhys. Lett. 81, no. 5, 50003 (2008).
- Julia sets and chaotic tunneling I. (with A. Shudo and K. S. Ikeda)
J. Phys. A: Math. Theor. 42, article number 265101 (26pp), (2009).
- Julia sets and chaotic tunneling II. (with A. Shudo and K. S. Ikeda)
J. Phys. A: Math. Theor. 42, article number 265102 (34pp), (2009).
Lecture notes etc†
- On some results of Bedford and Smillie concerning the complex dynamics of C^2. (in Japanese)
Kyoto University RIMS Kokyuroku, No. 1042, pp. 193-220 (1998).
- Physical phenomena and complex dynamics. (in Japanese)
Suuri Kagaku (2002).
- Dynamics of the complex Henon maps and the first tangency problem (after Bedford and Smillie).
Notes for lectures at Ryukoku University (2002).
- Discrete integrable systems and discrete dynamical systems. (in Japanese)
Suuri Kagaku (2003).
Books†
- Japanese translation of "An Introduction to Chaotic Dynamical Systems" by R. Devaney (with H. Kokubu, M. Kisaka and S. Nii).
Kyoritsu Publisher.
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