{
  "id": "1503.05175",
  "version": "v1",
  "published": "2015-03-17T19:23:48.000Z",
  "updated": "2015-03-17T19:23:48.000Z",
  "title": "Return- and hitting-time distributions of small sets in infinite measure preserving systems",
  "authors": [
    "Simon Rechberger",
    "Roland Zweimüller"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study convergence of return- and hitting-time distributions of small sets in recurrent dynamical systems preserving an infinite measure $\\mu$. In the presence of a Darling-Kac set with regularly varying wandering rate there is a scaling function suitable for all its subsets. In this case, we show that return distributions for a sequence $(E_{k})$ of sets with $\\mu(E_{k})\\rightarrow 0$ converge iff the corresponding hitting time distributions do, and we derive an explicit relation between the two limit laws. Some consequences of this result are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-17T19:23:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28D05",
      "37A05",
      "37C99"
    ],
    "keywords": [
      "infinite measure preserving systems",
      "small sets",
      "hitting-time distributions",
      "darling-kac set",
      "recurrent dynamical systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}