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

BUZZI, Jérôme ; FISHER, Todd ; TAHZIBI, Ali

Annales scientifiques de l'École normale supérieure, 2022, Vol.55 (4), p.969-1002 [Periódico revisado por pares]

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Título:
A dichotomy for measures of maximal entropy near time-one maps of transitive Anosov flows
Autor: BUZZI, Jérôme ; FISHER, Todd ; TAHZIBI, Ali
Assuntos: Dynamical Systems ; Mathematics
É parte de: Annales scientifiques de l'École normale supérieure, 2022, Vol.55 (4), p.969-1002
Descrição: 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.
Editor: Société mathématique de France
Idioma: Inglês

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