Growth rate of periodic orbits for geodesic flows oversurfaces with radially symmetric focusing caps

Bryce Weaver

doi:10.3934/jmd.2014.8.139

Article Contents

2014, Volume 8, Issue 2: 139-176. Doi: 10.3934/jmd.2014.8.139

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Growth rate of periodic orbits for geodesic flows over surfaces with radially symmetric focusing caps

Bryce Weaver^1,

1.
Department of Mathematics, Indiana University, Rawles Hall, 831 East 3rd St, Bloomington, IN 47405

Received: October 31, 2011

Revised: July 31, 2014

Published: October 2014

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Abstract

We obtain a precise asymptotic formula for the growth rate of periodic orbits of the geodesic flow over metrics on surfaces with negative curvature outside of a disjoint union of radially symmetric focusing caps of positive curvature. This extends results of G. Margulis and G. Knieper for negative and nonpositive curvature respectively.

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Mathematics Subject Classification: Primary: 37C27; Secondary: 53D25, 37D25.

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