SRB MEASURES FOR ALMOST AXIOM A DIFFEOMORPHISMS

José F. Alves (1) , Renaud Leplaideur (2)

1 Departamento de Matematica, Faculdade de Ciencias da Universidade do Porto
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

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 a probability SRB measure.

Mots clés: almost Axiom A; SRB measure

Domaines: Systèmes dynamiques [math.DS]

José F. Alves, Renaud Leplaideur. SRB MEASURES FOR ALMOST AXIOM A DIFFEOMORPHISMS. 2013. ⟨hal-00778407⟩