Homoclinic classes of geodesic flows on rank 1 manifolds

Abstract

Given a $C^{1+\beta }$ flow $\phi$ with positive speed on a closed smooth Riemannian manifold, we code two homoclinically related $\phi$-invariant probabilities by an irreducible countable topological Markov flow. As an application, we give proofs using symbolic dynamics of the theorem of Knieper on the uniqueness of the measure of maximal entropy and theorems of Burns et al on the uniqueness of equilibrium states.

10 pages, to appear in Proceedings of the AMS