{
  "id": "math/0509630",
  "version": "v2",
  "published": "2005-09-27T13:32:17.000Z",
  "updated": "2006-12-22T07:17:06.000Z",
  "title": "Topological pressure via saddle points",
  "authors": [
    "Katrin Gelfert",
    "Christian Wolf"
  ],
  "comment": "19 pages, Replaced with revised version, Accepted for publication in Trans. Amer. Math. Soc",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $\\Lambda$ 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 $P_{\\rm top}(\\phi)$ (with respect to the dynamical system $f|\\Lambda$) for a wide class of H\\\"older 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 $\\phi$ is entirely determined by the values of $\\phi$ on the saddle points of $f$ in $\\Lambda$. 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 $\\Lambda$. Our results generalize several well-known results to certain non-uniformly hyperbolic systems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-12-22T07:17:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37D35",
      "37C25",
      "37C45"
    ],
    "keywords": [
      "saddle points",
      "topological pressure",
      "mild nonuniform hyperbolicity assumption",
      "compact locally maximal invariant set",
      "smooth riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9630G"
    }
  }
}