Pressures for geodesic flows of rank one manifolds

Abstract

We study the geodesic flow on the unit tangent bundle of a rank one manifold and we give conditions under which all classical definitions of pressure of a Hölder continuous potential coincide. We provide a large deviation statement, which allows one to neglect (periodic) orbits that lack sufficient hyperbolic behaviour. Our results involve conditions on the potential, which take into consideration its properties in the non-hyperbolic part of the manifold. We draw some conclusions for the construction of equilibrium states. © 2014 IOP Publishing Ltd & London Mathematical Society.