Abstract
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.
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Egloff, D. On the Dynamics of Uniform Finsler Manifolds of Negative Flag Curvature. Annals of Global Analysis and Geometry 15, 101–116 (1997). https://doi.org/10.1023/A:1006576822477
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DOI: https://doi.org/10.1023/A:1006576822477