On the distribution of periodic orbits
| dc.creator | Gelfert, Katrin | |
| dc.creator | Wolf, Christian | |
| dc.date | 2009-01-14 | |
| dc.date.accessioned | 2026-07-07T12:29:36Z | |
| dc.date.available | 2026-07-07T12:29:36Z | |
| dc.description | Let $f:M\to M$ be a $C^{1+ε}$-map on a smooth Riemannian manifold $M$ and let $Λ\subset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of $f|Λ$. These results are non-invertible and, in particular, non-uniformly hyperbolic versions of well-known results by Bowen, Ruelle, and others in the case of hyperbolic diffeomorphisms. We show that the topological pressure $P_{\rm top}(φ)$ can be computed by the values of the potential $φ$ on the expanding periodic orbits and also that every hyperbolic ergodic invariant measure is well-approximated by expanding periodic orbits. Moreover, we prove that certain equilibrium states are Bowen measures. Finally, we derive a large deviation result for the periodic orbits whose time averages are apart from the space average of a given hyperbolic invariant measure. | |
| dc.identifier | https://arxiv.org/abs/0901.2139 | |
| dc.identifier | http://arxiv.org/abs/0901.2139 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215932 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37D25; 37D35 | |
| dc.title | On the distribution of periodic orbits | |
| dc.type | text |