Topological pressure via saddle points
| dc.creator | Gelfert, Katrin | |
| dc.creator | Wolf, Christian | |
| dc.date | 2005-09-27 | |
| dc.date | 2006-12-22 | |
| dc.date.accessioned | 2026-07-07T07:36:48Z | |
| dc.date.available | 2026-07-07T07:36:48Z | |
| dc.description | Let $Λ$ be a compact locally maximal invariant set of a $C^2$-diffeomorphism $f:M\to M$ on a smooth Riemannian manifold $M$. In this paper we study the topological pressure $P_{\rm top}(ϕ)$ (with respect to the dynamical system $f|Λ$) for a wide class of Hölder continuous potentials and analyze its relation to dynamical, as well as geometrical, properties of the system. We show that under a mild nonuniform hyperbolicity assumption the topological pressure of $ϕ$ is entirely determined by the values of $ϕ$ on the saddle points of $f$ in $Λ$. Moreover, it is enough to consider saddle points with ``large'' Lyapunov exponents. We also introduce a version of the pressure for certain non-continuous potentials and establish several variational inequalities for it. Finally, we deduce relations between expansion and escape rates and the dimension of $Λ$. Our results generalize several well-known results to certain non-uniformly hyperbolic systems. | |
| dc.description | 19 pages, Replaced with revised version, Accepted for publication in Trans. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0509630 | |
| dc.identifier | http://arxiv.org/abs/math/0509630 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120556 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37D25; 37D35; 37C25; 37C45 | |
| dc.title | Topological pressure via saddle points | |
| dc.type | text |