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A lower bound for topological entropy of generic non-Anosov symplectic diffeomorphisms

CATALAN, THIAGO ; TAHZIBI, ALI

Ergodic theory and dynamical systems, 2014-10, Vol.34 (5), p.1503-1524 [Periódico revisado por pares]

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Título:
A lower bound for topological entropy of generic non-Anosov symplectic diffeomorphisms
Autor: CATALAN, THIAGO ; TAHZIBI, ALI
Assuntos: Asymptotic methods ; Dynamical systems ; Entropy ; Ergodic processes ; Lower bounds ; Lyapunov exponents ; Preserving ; Topological manifolds ; Topology
É parte de: Ergodic theory and dynamical systems, 2014-10, Vol.34 (5), p.1503-1524
Notas: ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
Descrição: We prove that a ${C}^{1} $ generic symplectic diffeomorphism is either Anosov or its topological entropy is bounded from below by the supremum over the smallest positive Lyapunov exponent of its periodic points. We also prove that ${C}^{1} $ generic symplectic diffeomorphisms outside the Anosov ones do not admit symbolic extension and, finally, we give examples of volume preserving surface diffeomorphisms which are not points of upper semicontinuity of the entropy function in the ${C}^{1} $ topology.
Editor: Cambridge, UK: Cambridge University Press
Idioma: Inglês

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