On the Dynamics of Uniform Finsler Manifolds of Negative Flag Curvature

The geodesic flow of a compact Finsler manifold with negative flag curvature is an Anosov flow [23]. We use the structure of the stable and unstable foliation to equip the geodesic ray boundary of the universal covering with a Hölder structure. Gromov's geodesic rigidity and the Theorem of Dinaburg--Manning on the relation between the topological entropy and the volume entropy are generalized to the case of Finsler manifolds.