Generic measures for hyperbolic flows on non compact spaces

Abstract

We consider the geodesic flow on a complete connected negatively curved manifold. We show that the set of invariant borel probability measures contains a dense $G_{\delta }$-subset consisting of ergodic measures fully supported on the non-wandering set. We also trat the case of non-positively curved manifolds and provide general tools to deal with hyperbolic systems defined on non-compact spaces.