A relation between entropy and transitivity of Anosov diffeomorphisms

2022/03/16 by Micena, F. · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.08934

Abstract

It is known that transitive Anosov diffeomorphisms have a unique measure of maximal entropy (MME). Here we discuss the converse question. Under suitable hypothesis on Lyapunov exponents on the set of periodic points and the structure of the MME we get transitivity of C¹-Anosov diffeomorphisms.

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• Spectral decomposition and entropy for open set-valued maps

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