Counting closed geodesics on rank one manifolds

Details Counting closed geodesics on rank one manifolds Counting closed geodesics on rank one manifolds

2007-06-19

arxiv.org/abs/0706.2845v1

Mathematics

Dynamical Systems

36 pages, 2 figures. See also http://www.math.uni-hamburg.de/home/gunesch/

Scientific paper

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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