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arXiv · 0706.2845

Counting closed geodesics on rank one manifolds

Roland Gunesch
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Abstract

We establish a precise asymptotic formula for the number of homotopy classes of periodic orbits for the geodesic flow on rank one manifolds of nonpositive curvature. This extends a celebrated result of G. A. Margulis to the nonuniformly hyperbolic case and strengthens previous results by G. Knieper. We also establish some useful properties of the measure of maximal entropy.

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Roland Gunesch. 2007-06-19. Counting closed geodesics on rank one manifolds. https://arxiv.org/abs/0706.2845

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