Journal of Modern Dynamics (JMD)

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

Pages: 139 - 176, Issue 2, June 2014      doi:10.3934/jmd.2014.8.139

       Abstract        References        Full Text (419.8K)       Related Articles       

Bryce Weaver - Department of Mathematics, Indiana University, Rawles Hall, 831 East 3rd St, Bloomington, IN 47405, United States (email)

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.

Keywords:  Geodesic flows, nonuniformly hyperbolic systems, periodic orbits.
Mathematics Subject Classification:  Primary: 37C27; Secondary: 53D25, 37D25.

Received: November 2011;      Revised: August 2014;      Available Online: November 2014.