1. |
Keigo Matsumoto, Nami Ogawa, Hiroyuki Inou, Shizuo Kaji, Yutaka Ishii, Michitaka Hirose, Polyvision 4D space manipulation through multiple projections, *SIGGRAPH Asia 2019 Emerging Technologies - International Conference on Computer Graphics and Interactive Techniques, SA 2019
SIGGRAPH Asia 2019 Emerging Technologies, SA 2019*, 10.1145/3355049.3360518, 36-37, 2019.11, Seeing is believing. Our novel virtual reality system, Polyvision, applies this old saying to the fourth dimension. Various shadows of an object in a four-dimensional (4D) space are simultaneously projected onto multiple three-dimensional (3D) screens created in a virtual environment to reveal its intricate shape. The understanding of high-dimensional shapes and data can essentially be enhanced when good visualization is complemented by interactive functionality. However, a method to implement an interface for handling complex 4D transformations in a user-friendly manner must be developed. Using our Polyvision system, the user can manipulate each shadow as if it were a 3D object in their hand. The user’s action on each projection is reflected to the original 4D object, and in turn its projections, in real time. While controlling the object’s orientation minutely on one shadow, the user can grasp its global structure from multiple changing projections. Our system has a wide variety of applications in visualization, education, mathematical research, and entertainment, as we demonstrate with a variety of 4D objects that appear in mathematics and data sciences.. |

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Yutaka ISHII, Yutaro HIMEKI, M_4 is regular-closed., *Ergod. Th. & Dynam. Sys.*, 2020.01. |

3. |
Zin Arai, Yutaka Ishii, Hiroki Takahasi, Boundary of the horseshoe locus for the H'enon family, *SIAM J. Appl. Dyn. Syst.*, 17, 3, 2234-2248, 2018.04. |

4. |
Zin ARAI, Yutaka ISHII, On parameter loci of the H'enon family., *Commun. Math. Phys.*, 2018.12, We characterize the hyperbolic horseshoe locus and the maximal entropy locus of the Henon family. The proof employs a combination of complex analytic and complex dynamical methods together with rigorous numerics.. |

5. |
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.. |

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Yutaka ISHII, Hyperbolic polynomial diffeomorphisms of C^2. III: Iterated monodromy groups., *Advances in Mathematics*, 255, 242-304, 2014.01. |

7. |
Yutaka Ishii, Corrigendum to ``Hyperbolic polynomial diffeomorphisms of C^2. II: Hubbard trees.'', *Advances in Mathematics*, 226, 4, 3850-3855, 2011.07. |

8. |
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.. |

9. |
Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda, Julia sets and chaotic tunneling II., *J. Phys. A: Math. Theor.*, 42, article number 265102., 2009.06. |

10. |
Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda, Julia sets and chaotic tunneling I., *J. Phys. A: Math. Theor. *, 42, article number 265101., 2009.06. |

11. |
Yutaka Ishii, Hyperbolic polynomial diffeomorphisms of C^2. II: Hubbard trees., *Advances in Mathematics*, 220, 4, 985-1022, 2009.05. |

12. |
Yutaka Ishii, Hyperbolic polynomial diffeomorphisms of C^2. I: A non-planar map., *Advances in Mathematics*, 218, 2, 417-464, 2008.04. |

13. |
Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda, Chaos attracts tunneling trajectories: A universal mechanism of chaotic tunneling., *Europhysics Letters*, 81, pp. 50003., 2008.01. |

14. |
Yutaka Ishii, Duncan Sands, Lap number entropy formula for piecewise affine and projective maps., *Nonlinearity*, 20, pp. 2755--2772., 2007.01. |

15. |
Yutaka Ishii, Note on a paper by Kawasaki and Sasa on Bernoulli coupled map lattices. , *Journal of Physics A: Mathematical and General*, vol. 39, no. 45, 14043--14046., 2006.01. |

16. |
Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda, Julia set describes quantum tunnelling in the presence of chaos., *Journal of Physics A: Mathematical and General*, 10.1088/0305-4470/35/17/101, 35, 17, L225-L231, Vol. 35, no 17, L225-L231., 2002.01. |

17. |
Yutaka Ishii, Duncan Sands, Monotonicity of the Lozi family near the tent-maps., *Communications in Mathematical Physics*, Vol. 198, no. 2, pp. 397--406., 1998.01. |

18. |
Yutaka Ishii, Towards a kneading theory for Lozi mappings. II: Monotonicity of the topological entropy and Hausdorff dimension of attractors., *Communications in Mathematical Physics*, Vol. 190, no. 2, pp. 375--394., 1997.01. |

19. |
Yutaka Ishii, Towards a kneading theory for Lozi mappings I: A solution of the pruning front conjecture and the first tangency problem., *Nonlinearity*, Vol. 10, no. 3, pp. 731--747., 1997.01. |

20. |
Yutaka Ishii, Ising models, Julia sets, and similarity of the maximal entropy measures., *J.Statist.Phys.*, Vol. 78, no. 3-4, pp. 815--825., 1995.01. |