yutaka の履歴(No.39)

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Yutaka ISHII (石井 豊)

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(Caf'e Daguerre at Paris, March 2011)

Associate Professor
Department of Mathematics, Kyushu University
Motooka, Fukuoka 819-0395, Japan
Email: yutaka_at_math_dot_kyushu-u_dot_ac_dot_jp

Number of visitors to this webpage: 1055

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.
  Title of the thesis: A kneading theory for Lozi mappings.
  Advisor: Professor Mitsuhiro Shishikura (currently at Kyoto University)

Positions held†

• JSPS research fellow (DC1), University of Tokyo, April 1994 - March 1997.
• Research associate, Department of Mathematics, Kyushu University, January 1998 - August 2003.
  
• Maitre de conf'erence (mois d'invit'e), Universit'e Paris-Sud (Orsay), France, March 2002 - April 2002.
  
• Associate professor, Department of Mathematics, Kyushu University, September 2003 - to date.
  

Lecture series†

• "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 Paris-Sud (Orsay), France, July 1994 - August 1996.
• IMS, SUNY at Stony Brook, USA, November 1997 - December 1997.
• Cornell University, USA, October 1999 - September 2000.
• Universit'e Paris-Sud (Orsay), France, March 2001.
• Cornell University, USA, September 2001.
• Universit'e Paris-Sud (Orsay), France, March 2002 - April 2002.
• RIMS, Kyoto University, Japan, September 2003 - December 2003.
• Institut Henri Poincar'e, France, January 2004 - February 2004.
• 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.
• Yi-Chiuan Chen (Academia Sinica, Taiwan), November - December 2006.
• Anton Zorich (Universit'e de Rennes, France), May 2008.
• David Burguet (Ecole Normale Superieure Cachan, France), September 2011.
• Yi-Chiuan Chen (Academia Sinica, Taiwan), October 2011.
• Volodymyr Nekrashevych (Texas A&M University, USA), January 2012.

Research areas†

Dynamical systems (in particular, low-dimensional dynamics, symbolic dynamics, and complex dynamics).

Key words are; 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†

H'enon 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.
  Preprint (2011).

• On the parameter loci of the H'enon family. (with Z. Arai)
  In preparation (2012).

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).
  See also the comments on this article.

• 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 (2012).

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 H'enon 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).

• Describing the Julia sets by group actions. (in Japanese)
  Notes for a lecture in an annual meeting of the Mathematical Society of Japan (2008).

• Review of a paper by Sarah Koch.
  A document for Mathematical Reviews (2011).

Books†

• Japanese translation of "An Introduction to Chaotic Dynamical Systems" by R. Devaney (with H. Kokubu, M. Kisaka and S. Nii).
  Kyoritsu Publisher.

Travel Plans†

2013†

• Dynamics and Semialgebraic Geometry, July 8 - 12, RIMS at Kyoto University, Kyoto, Japan
  

2012†

• Integrated Research on Complex Dynamics, January 23 - 25, RIMS at Kyoto University, Kyoto, Japan
  
• Research visit, March 4 - 9, University of Tokyo, Tokyo, Japan
  
• Recent Progress in Lagrangian & Hamiltonian Dynamics, June 3 - 11, Ecole Normale Superi'eure de Lyon, Lyon, France
  
• Dynamics School on differential Galois theory, September 14 - 17, Kyushu Seminar House, Kuju, Japan
  
• Annual meeting of the Mathematical Society of Japan, September 18 - 21, Kyushu University, Fukuoka, Japan
  
• Informal seminar, November 25 - December 2, Harvard University, Boston, USA
  
• New Progress in Complex Dynamical Systems, December 10 - 14, RIMS at Kyoto University, Kyoto, Japan
  

2011†

• S'eminaire de Th'eorie Ergodique, January 9 - 11, Universit'e de Rennes, Rennes, France
  
• Ergodic Theory and Dynamical Systems Seminar, January 24 - 25, Warwick University, Coventry, UK
  
• S'eminaire de Th'eorie Ergodique, February 1, Universit'e de Paris VI (Jussieu), Paris, France
  
• Seminario di Sistemi Dinamici Olomorfi, February 9 - 11, Scuola Normale Superiore, Pisa, Italy
  
• SIAM Conference on Applications of Dynamical Systems, May 21 - 26, Snowbird Ski and Summer Resort, Snowbird, USA
  
• Kyoto Symposium on Complex Analysis in Several Variables XIV, July 18 - 21, Kyoto University, Kyoto, Japan
  
• G"ottingen-Penn State International Summer School, August 7 - 14, Georg-August-Universit"at G"ottingen, G"ottingen, Germany
  
• Summer School on Entropy Structure, September 19 - 23, Kyoto University, Kyoto, Japan
  
• Symposium on Complex Analysis, October 8 - 10, Chiba University, Chiba, Japan
  
• Frontiers in Dynamical Systems and Topology, November 21 - 25, RIMS at Kyoto University, Kyoto, Japan
  
• Automorphisms of Algebraic Varieties, December 19 - 23, Hotel Laforet, Shirahama, Japan
  

2010†

• Dynamics Seminar, January 29 - 30, Kyoto University, Kyoto, Japan
  
• Alg'ebre Dynamique et Topologie, June 13 - 15, Universit'e de Provence, Marseille, France
  
• Research visit, August 24 - 26, Georg-August-Universit"at G"ottingen, G"ottingen, Germany
  
• S'eminaire COOL, October 22, Institut Henri Poincar'e, Paris, France
  
• S'eminaire de Syst`emes Dynamiques, October 29, Universit'e de Paris VI & VII (Chevaleret), Paris, France
  
• S'eminaire de G'eom'etrie Ergodique, November 8, Ecole Polytechnique, Palaiseau, France
  
• Groupe de travail, November 15, Universit'e Paris-Sud (Orsay), Orsay, France