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In this paper we study aspects of the ergodic theory of the geodesic flow ona non-compact negatively curved manifold. It is a well known fact that everycontinuous potential on a compact metric space has a maximizing measure.Unfortunately, for non-compact spaces this fact is not longer true. For thegeodesic flow we provide a criterion that ensures the existence of a maximizingmeasure for uniformly continuous potentials. We prove that the only obstructionto the existence of a maximizing measure is the full escape of mass phenomenon.To the best of our knowledge, this is the first general result on the existenceof maximizing measures for non-compact topological spaces which does notrequire the potential to be coercive. We study zero temperature limits ofequilibrium measures for a suitable family of potentials. We prove someconvergence and divergence results for the limiting behaviour of such measures.Among some consequences we obtain that the geodesic flow has the intermediateentropy property and that equilibrium states are dense in the space ofinvariant probability measures.

Ergodic optimization and zero temperature limits in negative curvature