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

2023/03/10 by Keisuke Fujioka, Ryota Kogawa, Fujioka, Keisuke +5
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2303.05769

openalex publication_date 2023/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

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