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

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


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