Topological entropy of minimal geodesics and volume growth on surfaces
Eva Glasmachers Gerhard Knieper Carlos Ogouyandjou Jan Philipp Schröder
Journal of Modern Dynamics 2014, 8(1): 75-91 doi: 10.3934/jmd.2014.8.75
Let $(M,g)$ be a compact Riemannian manifold of hyperbolic type, i.e $M$ is a manifold admitting another metric of strictly negative curvature. In this paper we study the geodesic flow restricted to the set of geodesics which are minimal on the universal covering. In particular for surfaces we show that the topological entropy of the minimal geodesics coincides with the volume entropy of $(M,g)$ generalizing work of Freire and Mañé.
keywords: volume growth. topological entropy Geodesic flows on surfaces

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