Coupled H\'enon Map, Part I: Topological Horseshoes and Uniform Hyperbolicity

Keisuke Fujioka; Ryota Kogawa; Jizhou Li; Akira Shudo

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arXiv · 2303.05769

Coupled H\'enon Map, Part I: Topological Horseshoes and Uniform Hyperbolicity

Keisuke Fujioka·Ryota Kogawa·Jizhou Li·Akira Shudo

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Abstract

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 H\'enon maps via linear terms. The coupled H\'enon 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.

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Keisuke Fujioka, Ryota Kogawa, Jizhou Li, Akira Shudo. 2023-03-10. Coupled H\'enon Map, Part I: Topological Horseshoes and Uniform Hyperbolicity. https://arxiv.org/abs/2303.05769

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