Geodesic flow on Finsler manifolds of hyperbolic type

Abstract

Let (X,F) be a compact Finsler (no reversibility is assumed) manifold and X ̃ be its Finsler universal covering. In this work we study the geodesic flow restricted to the set of all geodesics that are minimal on X ̃. In particular we give a comparison result between the topological entropy and the volume entropy of (X, F ).