SRB measures of singular hyperbolic attractors

SRB measures for certain almost hyperbolic diffeomorphisms

The explosion of singular hyperbolic attractors

A singular hyperbolic attractor for flows is a partially hyperbolic at-tractor with singularities (hyperbolic ones) and volume expanding central direction [MPP1]. The geometric Lorenz attractor [GW] is an example of a singular hyperbolic attractor. In this paper we study the perturbations of singular hyperbolic attractors for three-dimensional flows. It is proved that any attractor obtained fro...

Topological dimension of singular - hyperbolic attractors

An attractor is a transitive set of a flow to which all positive orbit close to it converges. An attractor is singular-hyperbolic if it has singularities (all hyperbolic) and is partially hyperbolic with volume expanding central direction [16]. The geometric Lorenz attractor [6] is an example of a singular-hyperbolic attractor with topological dimension ≥ 2. We shall prove that all singular-hyp...

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...

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...