Homoclinic classes of geodesic flows on rank 1 manifolds

Yuri Lima, Mauricio Poletti

Published 2024-03-06, updated 2024-09-18Version 2

Given a $C^{1+\beta}$ flow $\varphi$ with positive speed on a closed smooth Riemannian manifold, we code two homoclinically related $\varphi$-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.