Isochronous and period-doubling diagrams for symplectic maps of the plane

T. Zolkin, S. Nagaitsev, I. Morozov, S. Kladov and Y.-K. Kim

Chaos, Solitons & Fractals, 2025, vol. 198, issue C

Abstract: Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the interpretation of how systems evolve under varying conditions. While the area-preserving quadratic Hénon map has received significant theoretical attention, a comprehensive description of its mixed parameter-space dynamics remain lacking. This limitation arises from early attempts to reduce the full two-dimensional phase space to a one-dimensional projection, a simplification that resulted in the loss of important dynamical features. Consequently, there is a clear need for a more thorough understanding of the underlying qualitative aspects.

Keywords: Chaos; Integrability; Perturbation theory; Stability (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925005260

DOI: 10.1016/j.chaos.2025.116513

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