{
  "id": "2106.07450",
  "version": "v1",
  "published": "2021-06-14T14:20:46.000Z",
  "updated": "2021-06-14T14:20:46.000Z",
  "title": "Local connectivity of the Julia sets with bounded type Siegel disks",
  "authors": [
    "Shuyi Wang",
    "Fei Yang",
    "Gaofei Zhang",
    "Yanhua Zhang"
  ],
  "comment": "32 pages, 10 figures",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We prove that the Julia sets of a number of rational maps and transcendental entire functions with bounded type Siegel disks are locally connected. This is based on establishing an expanding property of a long iteration of a class of quasi-Blaschke models near the unit circle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-14T14:20:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded type siegel disks",
      "julia sets",
      "local connectivity",
      "transcendental entire functions",
      "rational maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}