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Article Dans Une Revue Annales Scientifiques de l'École Normale Supérieure Année : 2022

A dichotomy for measures of maximal entropy near time-one maps of transitive Anosov flows

Une dichotomie pour les mesures d'entropie maximale près de l'application du temps 1 d'un flot d'Anosov transitif

Résumé

We show that time-one maps of transitive Anosov flows of compact manifolds are accumulated by diffeomorphisms robustly satisfying the following dichotomy: either all of the measures of maximal entropy are non-hyperbolic, or there are exactly two ergodic measures of maximal entropy, one with a positive central exponent and the other with a negative central exponent. We establish this dichotomy for certain partially hyperbolic diffeomorphisms isotopic to the identity whenever both of their strong foliations are minimal. Our proof builds on the approach developed by Margulis for Anosov flows where he constructs suitable families of measures on the dynamical foliations.
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Dates et versions

hal-03099935 , version 1 (23-05-2024)

Identifiants

Citer

Jérôme Buzzi, Todd Fisher, Ali Tahzibi. A dichotomy for measures of maximal entropy near time-one maps of transitive Anosov flows. Annales Scientifiques de l'École Normale Supérieure, 2022, 55 (4), pp.969-1002. ⟨10.24033/asens.2511⟩. ⟨hal-03099935⟩
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