Speaker: Roland Gunesch

Title:

Precise asypmtotics of periodic orbits for the geodesic flow in
nonpositive curvature

Abstract:

We establish an asymptotic formula for the number of homotopy classes of
periodic orbits for the geodesic flow on a manifold of nonpositive
curvature.  This extends a celebrated result of G.A. Margulis to the
nonuniformly hyperbolic case and strengthens previous results by G.
Knieper.  It is the most precise formula of this type that exists.

While proving this result, we also manage to carry out Margulis'
construction of the measure of maximal entropy without requiring strong
hyperbolicity.