Counting geodesics on a Riemannian manifold and topological entropy of geodesic flows
| dc.creator | Burns, Keith | |
| dc.creator | Paternain, Gabriel | |
| dc.date | 1996-10-25 | |
| dc.date.accessioned | 2026-07-07T09:15:38Z | |
| dc.date.available | 2026-07-07T09:15:38Z | |
| dc.description | 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 $\leq T$. Mañé showed that the exponential growth rate of the integral of $n_{T}(p,q)$ over $M \times M$ is the topological entropy of the geodesic flow of $M$. In the present paper we exhibit an open set of metrics on the two-sphere for which the exponential growth rate of $n_{T}(p,q$ is less than the topological entropy of the geodesic flow for a positive measure set of $(p,q)\in M\times M$. This answers in the negative questions raised by Mañé. | |
| dc.identifier | https://arxiv.org/abs/math/9610223 | |
| dc.identifier | http://arxiv.org/abs/math/9610223 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153084 | |
| dc.subject | Dynamical Systems | |
| dc.title | Counting geodesics on a Riemannian manifold and topological entropy of geodesic flows | |
| dc.type | text |