Counting closed geodesics in a compact rank one locally CAT(0) space

Abstract

Let $X$ be a compact, geodesically complete, locally CAT(0) space such that the universal cover admits a rank one axis. Assume $X$ is not homothetic to a metric graph with integer edge lengths. Let $P_t$ be the number of parallel classes of oriented closed geodesics of length $\le t$; then $\underset{t\to \infty }{\lim }{P}_t/\frac{e^{ht}}{ht}=1$, where $h$ is the entropy of the geodesic flow on the space $SX$ of parametrized unit-speed geodesics in $X$.

23 pages