Invariance of entropy for maps isotopic to Anosov

Abstract

We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of ${\mathbb{T}}^d$ with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with controlled geometry) and such that their induced action on $H_1({\mathbb{T}}^d)$ is hyperbolic. In absence of the simplicity condition we construct a robustly transitive counter-example.

4 figures, 20 pages. Some corrections added to the new version

References in corpus (1)

• A survey on partially hyperbolic dynamics

Cited by in corpus (4)

• Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems
• On the continuity of topological entropy of certain partially hyperbolic diffeomorphisms
• Equilibrium states for maps isotopic to Anosov
• Hyperbolicity of maximal entropy measures for certain maps isotopic to Anosov