Stably ergodic dynamical systems and partial hyperbolicity

In this paper we show that a little hyperbolicity goes a long way toward guaranteeing stable ergodicity, and in fact may be necessary for it. Our main theorem may be interpreted as saying that the same phenomenon producing chaotic behavior (i.e., some hyperbolicity) also leads to robust statistical behavior. 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. © 1997 Academic Press.