{
  "id": "0809.2938",
  "version": "v2",
  "published": "2008-09-17T14:42:29.000Z",
  "updated": "2009-07-05T01:59:49.000Z",
  "title": "Entropy and Poincaré recurrence from a geometrical viewpoint",
  "authors": [
    "Paulo Varandas"
  ],
  "comment": "11 pages, revised version",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study Poincar\\'e recurrence from a purely geometrical viewpoint. We prove that the metric entropy is given by the exponential growth rate of return times to dynamical balls. This is the geometrical counterpart of Ornstein-Weiss theorem. Moreover, we show that minimal return times to dynamical balls grow linearly with respect to its length. Finally, some interesting relations between recurrence, dimension, entropy and Lyapunov exponents of ergodic measures are given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-05T01:59:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B20",
      "37A35",
      "37C45"
    ],
    "keywords": [
      "geometrical viewpoint",
      "exponential growth rate",
      "study poincare recurrence",
      "minimal return times",
      "metric entropy"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/22/10/003",
      "journal": "Nonlinearity",
      "year": 2009,
      "month": "Oct",
      "volume": 22,
      "number": 10,
      "pages": 2365
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009Nonli..22.2365V"
    }
  }
}