{
  "id": "2505.04944",
  "version": "v1",
  "published": "2025-05-08T04:48:26.000Z",
  "updated": "2025-05-08T04:48:26.000Z",
  "title": "Local connectivity of Julia sets of some transcendental entire functions with Siegel disks",
  "authors": [
    "Fei Yang",
    "Gaofei Zhang",
    "Yanhua Zhang"
  ],
  "comment": "23 pages, 3 figures; Partial results have been announced in arXiv:2106.07450v1",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Based on the weak expansion property of a long iteration of a family of quasi-Blaschke products near the unit circle established recently, we prove that the Julia sets of a number of transcendental entire functions with bounded type Siegel disks are locally connected. In particular, if $\\theta$ is of bounded type, then the Julia set of the sine function $S_\\theta(z)=e^{2\\pi i\\theta}\\sin(z)$ is locally connected. Moreover, we prove the existence of transcendental entire functions having Siegel disks and locally connected Julia sets with asymptotic values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-08T04:48:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transcendental entire functions",
      "julia set",
      "local connectivity",
      "weak expansion property",
      "bounded type siegel disks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}