Coexistence of chaotic and elliptic behaviors among analytic, symplectic diffeomorphisms of any surface

2021/05/18 by Pierre Berger, Berger, Pierre · 2 citations
Mathematics · Physics and Astronomy · #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS

paper · pdf · doi:10.48550/arxiv.2105.08354

arxiv created 2021/05/18 · openalex publication_date 2021/05/18 · arxiv updated 2021/05/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We show the coexistence of chaotic behaviors (positive metric entropy) and elliptic behaviors (intregrable KAM island) among analytic, symplectic diffeomorphism of any closed surface. In particilar this solves a problem by F. Przytycki (1982).

Cited by

• Wild dynamics on manifolds
• On Kolmogorov-typical properties of symplectic dynamics

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