English

Topological entropy of minimal geodesics and volume growth on surfaces

Differential Geometry 2013-08-12 v1 Dynamical Systems

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.

Keywords

Cite

@article{arxiv.1308.2127,
  title  = {Topological entropy of minimal geodesics and volume growth on surfaces},
  author = {Gerhard Knieper and Carlos Ogouyandjou and Jan Philipp Schröder},
  journal= {arXiv preprint arXiv:1308.2127},
  year   = {2013}
}

Comments

16 pages