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

DOI10.5802/JEP.224zbMath1521.37068arXiv2105.08354MaRDI QIDQ6367906

Publication date: 18 May 2021

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).

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46) Completely integrable discrete dynamical systems (37J70) Higher-dimensional holomorphic and meromorphic dynamics (37F80)

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