On the mixing and Bernoulli properties for geodesic flows on rank 1 manifolds without focal points

Fei Liu, Xiaokai Liu, Fang Wang

If $(M,g)$ is a smooth compact rank $1$ Riemannian manifold without focal points, it is shown that the measure ${\mu }_{\max }$ of maximal entropy for the geodesic flow is unique. In thi…