Counting closed geodesics on rank one manifolds

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.

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