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SRB measures for almost Axiom A diffeomorphisms

  • JOSÉ F. ALVES (a1) and RENAUD LEPLAIDEUR (a2)

Abstract

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.

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SRB measures for almost Axiom A diffeomorphisms

  • JOSÉ F. ALVES (a1) and RENAUD LEPLAIDEUR (a2)

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