Singular hyperbolicity for transitive attractors with singular points of 3-dimensional C2-flows

Abstract

In the context of C r -flows on 3-manifolds (r ≥ 1), the notion of singular hyperbolicity, inspired on the Lorenz Attractor, is the right generalization of hyperbolicity (in the sense of Smale) for C1-robustly transitive sets with singularities. We estabish conditions (on the associated linear Poincare flow and on the nature of the singular set) under which a transitive attractor with singularities of a C2-flow on a 3-manifold is singular hyperbolic.