{
  "id": "1007.3855",
  "version": "v2",
  "published": "2010-07-22T11:08:28.000Z",
  "updated": "2011-03-29T13:42:54.000Z",
  "title": "Bowen's formula for meromorphic functions",
  "authors": [
    "Krzysztof Barański",
    "Bogusława Karpińska",
    "Anna Zdunik"
  ],
  "comment": "26 pages",
  "journal": "Ergodic Theory Dynam. Systems 32 (2012), 1165-1189",
  "doi": "10.1017/S0143385711000290",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be an arbitrary transcendental entire or meromorphic function in the class $\\mathcal S$ (i.e. with finitely many singularities). We show that the topological pressure $P(f,t)$ for $t > 0$ can be defined as the common value of the pressures $P(f,t, z)$ for all $z \\in \\mathbb C$ up to a set of Hausdorff dimension zero. Moreover, we prove that $P(f,t)$ equals the supremum of the pressures of $f|_X$ over all invariant hyperbolic subsets $X$ of the Julia set, and we prove Bowen's formula for $f$, i.e. we show that the Hausdorff dimension of the radial Julia set of $f$ is equal to the infimum of the set of $t$, for which $P(f,t)$ is non-positive. Similar results hold for (non-exceptional) transcendental entire or meromorphic functions $f$ in the class $\\mathcal B$ (i.e. with bounded set of singularities), for which the closure of the post-singular set does not contain the Julia set.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-29T13:42:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F35"
    ],
    "keywords": [
      "meromorphic function",
      "bowens formula",
      "hausdorff dimension zero",
      "arbitrary transcendental entire",
      "invariant hyperbolic subsets"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.3855B"
    }
  }
}