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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2016

SRB measures for almost Axiom A diffeomorphisms

Résumé

We consider a diffeomorphism $f$ of a compact manifold $M$ which is almost Axiom A , i.e. $f$ is hyperbolic in a neighborhood of some compact $f$ -invariant set, except in some singular set of neutral points. We prove that if there exists some $f$ -invariant set of hyperbolic points with positive unstable Lebesgue measure such that for every point in this set the stable and unstable leaves are ‘long enough’, then $f$ admits an SRB (probability) measure.

Dates et versions

hal-03996435 , version 1 (19-02-2023)

Identifiants

Citer

José Alves, Renaud Leplaideur. SRB measures for almost Axiom A diffeomorphisms. Ergodic Theory and Dynamical Systems, 2016, 36 (7), pp.2015-2043. ⟨10.1017/etds.2015.4⟩. ⟨hal-03996435⟩
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