{
  "id": "math/0411492",
  "version": "v1",
  "published": "2004-11-22T18:41:06.000Z",
  "updated": "2004-11-22T18:41:06.000Z",
  "title": "Rational maps are $d$-adic Bernoulli",
  "authors": [
    "D. Heicklen",
    "C. Hoffman"
  ],
  "comment": "12 pages, published version",
  "journal": "Ann. of Math. (2), Vol. 156 (2002), no. 1, 103--114",
  "categories": [
    "math.DS"
  ],
  "abstract": "Freire, Lopes and Mane proved that for any rational map f there exists a natural invariant measure \\mu_f [5]. Mane showed there exists an n>0 such that (f^n, \\mu_f) is measurably conjugate to the one-sided $d^n$-shift, with Bernoulli measure $(\\frac 1{d^n},... ,\\frac 1{d^n})$ \\[15]. In this paper we show that (f,\\mu_f)is conjugate to the one-sided Bernoulli $d$-shift. This verifies a conjecture of Freire, Lopes and Mane [5] and Lyubich [11].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-22T18:41:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "28D05",
      "37A05",
      "37A35"
    ],
    "keywords": [
      "rational map",
      "adic bernoulli",
      "natural invariant measure",
      "bernoulli measure",
      "measurably conjugate"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11492H"
    }
  }
}