{
  "id": "0901.2139",
  "version": "v1",
  "published": "2009-01-14T23:05:04.000Z",
  "updated": "2009-01-14T23:05:04.000Z",
  "title": "On the distribution of periodic orbits",
  "authors": [
    "Katrin Gelfert",
    "Christian Wolf"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f:M\\to M$ be a $C^{1+\\epsilon}$-map on a smooth Riemannian manifold $M$ and let $\\Lambda\\subset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of $f|\\Lambda$. 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 $P_{\\rm top}(\\varphi)$ can be computed by the values of the potential $\\varphi$ 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-14T23:05:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37D35"
    ],
    "keywords": [
      "distribution",
      "expanding periodic orbits",
      "hyperbolic ergodic invariant measure",
      "large deviation result",
      "invariant locally maximal set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}