Srb Measures of Certain Almost Hyperbolic Diffeomorphisms with a Tangency

SRB measures for certain almost hyperbolic diffeomorphisms

Srb Measures for Almost Axiom a Diffeomorphisms

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 enoug...

Srb Measures for Weakly Expanding Maps

We construct SRB measures for endomorphisms satisfying conditions far weaker than the usual non-uniform expansion. As a consequence, the definition of a non-uniformly expanding map can be weakened. We also prove the existence of an absolutely continuous invariant measure for local diffeomorphisms, only assuming the existence of hyperbolic times for Lebesgue almost every point in the manifold.

Generalized Physical and Srb Measures for Hyperbolic Diffeomorphisms

In this paper we introduce the notion of generalized physical and SRB measures. These measures naturally generalize classical physical and SRB measures to measures which are supported on invariant sets that are not necessarily attractors. We then perform a detailed case study of these measures for hyperbolic Hénon maps. For this class of systems we are able to develop a complete theory about th...

A Criterion for Ergodicity of Non-uniformly Hyperbolic Diffeomorphisms

A. In this work we exhibit a new criteria for ergodicity of diffeomorphisms involving conditions on Lyapunov exponents and general position of some invariant manifolds. On one hand we derive uniqueness of SRB-measures for transitive surface diffeomorphisms. On the other hand, using recent results on the existence of blenders we give a positive answer, in the C topology, to a conjecture o...