Topological entropy of minimal geodesics and volume growth on surfaces

Eva Glasmachers, Gerhard Knieper, Carlos Ogouyandjou, Jan Philipp Schröder

Type: Article

Publication Date: 2014-01-01

Citations: 7

DOI: https://doi.org/10.3934/jmd.2014.8.75

Abstract

Let $(M,g)$ be a compact Riemannian manifold of hyperbolic type, i.e$M$ is a manifold admitting another metric of strictly negativecurvature. In this paper we study the geodesic flow restricted to theset of geodesics which are minimal on the universal covering. Inparticular for surfaces we show that the topological entropy of theminimal geodesics coincides with the volume entropy of $(M,g)$generalizing work of Freire and Mañé.

Locations

Journal of Modern Dynamics - View - PDF

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