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arXiv · 2001.05516

Invariance of entropy for maps isotopic to Anosov

Pablo D. Carrasco·Cristina Lizana·Enrique Pujals·Carlos H. Vásquez
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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.

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Pablo D. Carrasco, Cristina Lizana, Enrique Pujals, Carlos H. Vásquez. 2020-01-15. Invariance of entropy for maps isotopic to Anosov. https://doi.org/10.1088/1361-6544/abdfb3

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