{
  "id": "0812.4761",
  "version": "v2",
  "published": "2008-12-27T18:12:52.000Z",
  "updated": "2010-02-06T20:12:00.000Z",
  "title": "Large deviation principles for non-uniformly hyperbolic rational maps",
  "authors": [
    "Henri Comman",
    "Juan Rivera-Letelier"
  ],
  "comment": "Final version; to appear in Ergodic Theory and Dynamical Systems",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "We show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called \"Topological Collet-Eckmann\". More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic points, and Birkhoff averages. For this purpose we show that each H{\\\"o}lder continuous potential admits a unique equilibrium state, and that the pressure function can be characterized in terms of iterated preimages, periodic points, and Birkhoff averages. Then we use a variant of a general result of Kifer.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-06T20:12:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35",
      "37A50",
      "37D25",
      "60F10"
    ],
    "keywords": [
      "large deviation principle",
      "non-uniformly hyperbolic rational maps",
      "periodic points",
      "birkhoff averages",
      "iterated preimages"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4761C"
    }
  }
}