Volume asymptotics on rank one manifolds of nonpositive curvature

In this article, we consider a closed rank one Riemannian manifold $M$ of nonpositive curvature and its universal cover $X$. Let $b_t(x)$ be the Riemannian volume of the ball of radius $t>0$ around $x\in X$, and $h$ the topological entropy of the geodesic flow. We obtain the following Margulis-type asymptotic estimates \[\lim_{t\to \infty}b_t(x)/e^{ht}=c(x)\] for some continuous function $c: X\to \mathbb{R}$.