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 rank-one axis. Assume is not homothetic to metric graph with integer edge lengths. $P_t$ number of parallel classes oriented closed geodesics length at most t ; then $\lim \nolimits _{t \to \infty } P_t / ({e^{ht}}/{ht}) = 1$ , where h entropy geodesic flow on $GX$ parametrized unit-speed in .