Une nouvelle analyse des mesures maximisant l'entropie des diff\'eomorphismes d'Anosov de surfaces

TL;DR

This paper presents a new proof for the finite multiplicity of maximum entropy measures in surface Anosov diffeomorphisms, avoiding explicit Markov partition construction and applicable to broader non-uniform hyperbolic cases.

Contribution

It introduces an alternative proof method for maximum entropy measures in Anosov diffeomorphisms that bypasses traditional Markov partition techniques.

Findings

Finite multiplicity of maximum entropy measures established

New proof technique avoiding explicit Markov partitions

Applicable to non-uniform hyperbolic diffeomorphisms

Abstract

This note illustrates the strategy of our paper on piecewise affine surface homeomorphisms by giving a new proof of the finite multiplicity of the maximum entropy measure of Anosov diffeomorphisms (here on surfaces). This approach avoids the explicit construction of Markov partitions and will be applied elsewhere to some non-uniformly hyperbolic diffeomorphisms.