Homoclinic classes of geodesic flows on rank 1 manifolds

Source abstract

Given a C 1 + β C^{1+\beta } flow φ \varphi with positive speed on a closed smooth Riemannian manifold, we code two homoclinically related φ \varphi –invariant probabilities by an irreducible countable topological Markov flow. As an application, we give a proof using symbolic dynamics of the theorem of Knieper [Ann. of Math. (2) 148 (1998), pp. 291–314] on the uniqueness of the measure of maximal entropy and theorems of Burns et al. [Geom. Funct. Anal. 28 (2018), pp. 1209–1259] on the uniqueness of equilibrium states.