Diffeomorphisms admitting SRB measures and their regularity

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 certain almost hyperbolic diffeomorphisms

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...

Srb Measures of Certain Almost Hyperbolic Diffeomorphisms with a Tangency

We study topological and ergodic properties of some almost hyperbolic diffeomorphisms on two dimensional manifolds. Under generic conditions, diffeomorphisms obtained from Anosov by an isotopy pushing together the stable and unstable manifolds to be tangent at a fixed point, are conjugate to Anosov. For a finite codimension subset at the boundary of Anosov there exist a SRB measure and an uniqu...

Innnite Dimensional Srb Measures

We review the basic steps leading to the construction of a Sinai-Ruelle-Bowen (SRB) measure for an innnite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of space-time correlations. First, using the Perron-Frobenius operator, one connects the dynamical system of coupled maps on a d-dimensional lattice to an equilibrium statistical mechanical...