Asymptotic geometry and growth of conjugacy classes of nonpositively curved manifolds

Abstract

Let X be a Hadamard manifold and $Γ$ a discrete group of isometries of X which contains an axial isometry without invariant flat half plane. We study the behavior of conformal densities on the geometric limit set of $Γ$ in order to derive a new asymptotic estimate for the growth rate of closed geodesics in not necessarily compact or finite volume manifolds.