50 citations · 53 across the 5 of their papers we have counts for
5 papers
Pseudo-monodromy and the Mandelbrot set
Yutaka Ishii, Thomas Richards
We investigate the discontinuity of codings for the Julia set of a quadratic map. To each parameter ray, we associate a natural coding for Julia sets on the ray. Given a hyperbolic…
Boundary of the horseshoe locus for the Hénon family
Zin Arai, Yutaka Ishii, Hiroki Takahasi
The purpose of this article is to investigate geometric properties of the parameter locus of the Hénon family where the uniform hyperbolicity of a horseshoe breaks down. As an appl…
On parameter loci of the Hénon family
Zin Arai, Yutaka Ishii
The purpose of the current article is to investigate the dynamics of the Hénon family , where $(a, b)\in \mathbb{R}\times\mathbb{R}^{\times…
Homotopy shadowing
Yutaka Ishii, John Smillie
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 generaliz…
Julia set describes quantum tunneling in the presence of chaos
A. Shudo, Y. ishii, K. S. Ikeda
We find that characteristics of quantum tunneling in the presence of chaos can be regarded as a manifestation of the Julia set of the complex dynamical system. Several numerical ev…