{
  "id": "math/0405522",
  "version": "v11",
  "published": "2004-05-27T08:09:39.000Z",
  "updated": "2005-09-23T02:48:27.000Z",
  "title": "Dimensions of Julia sets of expanding rational semigroups",
  "authors": [
    "Hiroki Sumi"
  ],
  "comment": "31 pages, Revised on July 1, 2005. Some typos are fixed. The title was changed. See also http://www.math.sci.osaka-u.ac.jp/~sumi/",
  "journal": "Kodai Mathematical Journal (2005) Vol. 28, No.2, pp390-422",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in ergodic theory. Furthermore, we show Bowen's formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition. What we discuss is the `backward iterated function systems', and since the generator maps are not injective in general, we need some efforts to estimate the measure of disks.",
  "revisions": [
    {
      "version": "v11",
      "updated": "2005-09-23T02:48:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "expanding rational semigroups",
      "julia set",
      "generated expanding semigroup satisfying",
      "open set condition",
      "ergodic theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5522S"
    }
  }
}