Stable Ergodicity and Stable Accessibility

In this paper we discuss how a little hyperbolicity goes a long way towards guaranteeing stable ergodicity. Examples to which our theory applies include translations on certain homogeneous spaces and the time one map of the geodesic flow for a manifold of constant negative curvature. We also discuss the role played by a concept from control theory, accessibility by paths tangent to a pair of subbundles of the tangent bundle.