13 citations · 16 across the 3 of their papers we have counts for
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math.DS2018★ 1 cited
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…
math.DS2015★ 2 cited
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…
math.DS2007★ 13 cited
On Loops in the Hyperbolic Locus of the Complex Hénon Map and Their Monodromies
Zin Arai
We prove John Hubbard's conjecture on the topological complexity of the hyperbolic horseshoe locus of the complex Hénon map. Indeed, we show that there exist several non-trivial lo…