(1) Department of Mathematics, University of Houston, Houston, USA;(2) Department of Mathematics, University of North Carolina, Chapel Hill, USA;
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 Gδ-subset consisting of ergodic measures fully supported on the non-wandering set. We also treat the case of non-positively
curved manifolds and provide general tools to deal with hyperbolic systems defined on non-compact spaces.