2 papers
math.DS2024
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…
math.DS2018
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…