Coupled Hénon Map, Part I: Topological Horseshoes and Uniform Hyperbolicity

We derive a sufficient condition for topological horseshoe and uniform hyperbolicity of a 4-dimensional symplectic map, which is introduced by coupling the two 2-dimensional Hénon maps via linear terms. The coupled Hénon map thus constructed can be viewed as a simple map modeling the horseshoe in hi...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Fujioka, Keisuke, Kogawa, Ryota, Li, Jizhou, Shudo, Akira
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.03.2023
Subjects
Topology
Online AccessGet full text

Cover

More Information
Summary:We derive a sufficient condition for topological horseshoe and uniform hyperbolicity of a 4-dimensional symplectic map, which is introduced by coupling the two 2-dimensional Hénon maps via linear terms. The coupled Hénon map thus constructed can be viewed as a simple map modeling the horseshoe in higher dimensions. We show that there are two different types of horseshoes, each of which is realized around different anti-integrable limits in the parameter regime.
ISSN:2331-8422