{
  "id": "2407.14476",
  "version": "v1",
  "published": "2024-07-19T17:27:44.000Z",
  "updated": "2024-07-19T17:27:44.000Z",
  "title": "On postcritical sets of quadratic polynomials with a neutral fixed point",
  "authors": [
    "Hongyu Qu"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "The control of postcritical sets of quadratic polynomials with a neutral fixed point is a main ingredient in the remarkable work of Buff and Ch\\'eritat to construct quadratic Julia sets with positive area. Based on the Inou-Shishikura theory, they obtained the control for the case of rotation numbers of bounded high type. Later, Cheraghi developed several elaborate analytic techniques based on Inou-Shishikura's results and obtained the control for the case of rotation numbers of high type. In this paper, based on the pseudo-Siegel disk theory of Dudko and Lyubich, we obtained the control for the general case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-19T17:27:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neutral fixed point",
      "quadratic polynomials",
      "postcritical sets",
      "rotation numbers",
      "high type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}