Topological entropy of minimal geodesics and volume growth on surfaces

Gerhard Knieper; Carlos Ogouyandjou; Jan Philipp Schröder

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arXiv · 1308.2127

Topological entropy of minimal geodesics and volume growth on surfaces

Gerhard Knieper·Carlos Ogouyandjou·Jan Philipp Schröder

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Abstract

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 Mane.

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Gerhard Knieper, Carlos Ogouyandjou, Jan Philipp Schröder. 2013-08-09. Topological entropy of minimal geodesics and volume growth on surfaces. https://arxiv.org/abs/1308.2127

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