{
  "id": "2011.08267",
  "version": "v1",
  "published": "2020-11-16T20:48:07.000Z",
  "updated": "2020-11-16T20:48:07.000Z",
  "title": "Hausdorff dimension of escaping sets of meromorphic functions II",
  "authors": [
    "Magnus Aspenberg",
    "Weiwei Cui"
  ],
  "comment": "22 pages, 5 figures",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "A function which is transcendental and meromorphic in the plane has at least two singular values. On one hand, if a meromorphic function has exactly two singular values, it is known that the Hausdorff dimension of the escaping set can only be either $2$ or $1/2$. On the other hand, the Hausdorff dimension of escaping sets of Speiser functions can attain every number in $[0,2]$ (cf. \\cite{ac1}). In this paper, we show that number of singular values which is needed to attain every Hausdorff dimension of escaping sets is not more than $4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-16T20:48:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05",
      "37F31",
      "30D30"
    ],
    "keywords": [
      "hausdorff dimension",
      "escaping set",
      "meromorphic function",
      "singular values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}