{
  "id": "0807.0970",
  "version": "v1",
  "published": "2008-07-07T09:01:13.000Z",
  "updated": "2008-07-07T09:01:13.000Z",
  "title": "Poincaré recurrence for observations",
  "authors": [
    "Jerôme Rousseau",
    "Benoit Saussol"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "A high dimensional dynamical system is often studied by experimentalists through the measurement of a relatively low number of different quantities, called an observation. Following this idea and in the continuity of Boshernitzan's work, for a measure preserving system, we study Poincar\\'e recurrence for the observation. The link between the return time for the observation and the Hausdorff dimension of the image of the invariant measure is considered. We prove that when the decay of correlations is super polynomial, the recurrence rates for the observations and the pointwise dimensions relatively to the push-forward are equal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-07T09:01:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C45",
      "37B20",
      "37A25",
      "37M25"
    ],
    "keywords": [
      "observation",
      "high dimensional dynamical system",
      "study poincare recurrence",
      "relatively low number",
      "recurrence rates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.0970R"
    }
  }
}