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

Abstract

We prove that a $C^1-$generic symplectic diffeomorphism is either Anosov or the topological entropy is bounded from below by the supremum over the smallest positive Lyapunov exponent of the 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 diffeomorphisms which are not point of upper semicontinuity of entropy function in $C^1-$topology.

References in corpus (3)

• Symbolic extensions for partially hyperbolic diffeomorphisms
• Entropy-expansiveness for partially hyperbolic diffeomorphisms
• On the regularization of conservative maps

Cited by in corpus (5)

• A C1 generic condition for existence of symbolic extensions of volume preserving diffeomorphisms
• Local perturbations of conservative $C^1$-diffeomorphisms
• A link between Topological Entropy and Lyapunov Exponents
• Symbolic Extensions and dominated splittings for Generic C^1-Diffeomorphisms
• Entropy of partially hyperbolic flows with center dimension two