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Journal of Modern Dynamics (JMD)
 

Topological entropy of minimal geodesics and volume growth on surfaces

Pages: 75 - 91, Issue 1, March 2014      doi:10.3934/jmd.2014.8.75

 
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Eva Glasmachers - Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany (email)
Gerhard Knieper - Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany (email)
Carlos Ogouyandjou - Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey-Calavi 01 BP 613 Porto-Novo, Benin (email)
Jan Philipp Schröder - Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany (email)

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 Mañé.

Keywords:  Geodesic flows on surfaces, topological entropy, volume growth.
Mathematics Subject Classification:  Primary: 37A35, 37D40; Secondary: 53D25.

Received: August 2013;      Revised: March 2014;      Available Online: July 2014.

 References