{
  "id": "math/0410505",
  "version": "v2",
  "published": "2004-10-23T10:20:26.000Z",
  "updated": "2004-10-27T14:02:38.000Z",
  "title": "The Rokhlin lemma for homeomorphisms of a Cantor set",
  "authors": [
    "Sergey Bezuglyi",
    "Anthony H. Dooley",
    "Konstantin Medynets"
  ],
  "comment": "9 pages. Proc. Ams, to appear",
  "journal": "Proc. AMS 133 (2005), p. 2957-2964",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a Cantor set $X$, let $Homeo(X)$ denote the group of all homeomorphisms of $X$. The main result of this note is the following theorem. Let $T\\in Homeo(X)$ be an aperiodic homeomorphism, let $\\mu_1,\\mu_2,...,\\mu_k$ be Borel probability measures on $X$, $\\e> 0$, and $n \\ge 2$. Then there exists a clopen set $E\\subset X$ such that the sets $E,TE,..., T^{n-1}E$ are disjoint and $\\mu_i(E\\cup TE\\cup...\\cup T^{n-1}E) > 1 - \\e, i= 1,...,k$. Several corollaries of this result are given. In particular, it is proved that for any aperiodic $T\\in Homeo(X)$ the set of all homeomorphisms conjugate to $T$ is dense in the set of aperiodic homeomorphisms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-27T14:02:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37A40"
    ],
    "keywords": [
      "cantor set",
      "rokhlin lemma",
      "aperiodic homeomorphism",
      "borel probability measures",
      "main result"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10505B"
    }
  }
}