Boundary of the horseshoe locus for the henon family

Zin Arai, Yutaka Ishii, Hiroki Takahasi

Research output: Contribution to journalArticlepeer-review

Abstract

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 application, we obtain a variational characterization of equilibrium measures "at temperature zero" for the corresponding non-uniformly hyperbolic Hénon maps. The method of the proof also yields that the boundary of the hyperbolic horseshoe locus in the parameter space consists of two monotone pieces, which confirms a conjecture in [AI]. The proofs of these results are based on the machinery developed in [AI] which employs the complexification of both the dynamical and the parameter spaces of the Hénon family together with computer assistance.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Mar 25
Externally publishedYes

ASJC Scopus subject areas

  • General

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