Work

Topological horseshoe and uniform hyperbolicity of the symplectic coupled Hénon map

Year: 2025

Type: article

Abstract: We analyze topological horseshoe and uniform hyperbolicity of a 4-dimensional symplectic map, which is introduced by coupling the two 2-dimensional symplectic Hénonmaps via linear terms. Based on the cone field argument following Devaney and Nitecki, 1979), we first derive a sufficient condition for topological horseshoe and uniform hyperbolicity in the parameter space including the two different anti-integrable limits. We then explore uniformly hyperbolic parameter regions by applying the computer-assisted proof developed by Arai and find that there exist non-trivial uniformly hyperbolic regions in the parameter space that differ from those obtained using the cone condition. The existence of such non-trivial uniformly hyperbolic regions reminds us of the so-called hyperbolic plateaus in the two-dimensional Hénon map.

Source: Physica D Nonlinear Phenomena

DOI: 10.1016/j.physd.2025.134722

Authors: Keisuke Fujioka, Ryota Kogawa, Jizhou Li, Akira Shudo

Institutions: Tokyo Metropolitan University, RIKEN

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,640

Funders: Japan Society for the Promotion of Science, Japan Science and Technology Agency, Fusion Oriented REsearch for disruptive Science and Technology