Homoclinic classes for flows: Ergodicity and SRB measures

In this work we study homoclinic classes for some classes of flows, extending to flows certain results previously obtained, by other authors, for diffeomorphisms. More precisely, we prove that given a conservative C² flow φₜ:M→ M over a smooth compact Riemannian manifold M, if both the stable and unstable homoclinic classes of a certain periodic hyperbolic orbit γ have positive Lebesgue measure, then their intersection is an ergodic component of the flow. We also obtain analogous results for invariant SRB measures.