Counting geodesics on a Riemannian manifold and topological entropy of geodesic flows

Keith Burns, Gabriel Paternain

Let $M$ be a compact $C^{\infty }$ Riemannian manifold. Given $p$ and $q$ in $M$ and $T>0$, define $n_T(p,q)$ as the number of geodesic segments joining $p$ and $q$ with length $\…