Growth rate of periodic orbits for geodesic flows over surfaces with radially symmetric focusing caps
Bryce Weaver
Journal of Modern Dynamics 2014, 8(2): 139-176 doi: 10.3934/jmd.2014.8.139
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: nonuniformly hyperbolic systems periodic orbits. Geodesic flows

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