SRB measures for almost Axiom A diffeomorphisms

摘要

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.