{
  "id": "1205.2544",
  "version": "v3",
  "published": "2012-05-11T14:54:37.000Z",
  "updated": "2019-11-08T14:40:37.000Z",
  "title": "Hausdorff dimension of biaccessible angles for quadratic polynomials",
  "authors": [
    "Henk Bruin",
    "Dierk Schleicher"
  ],
  "comment": "Update to the published version",
  "journal": "Fundamenta Mathematicae 238 (2017)",
  "doi": "10.4064/fm276-6-2016",
  "categories": [
    "math.DS"
  ],
  "abstract": "A point $z$ in the Julia set of a polynomial $p$ is called biaccessible if two dynamic rays land at $z$; a point $z$ in the Mandelbrot set is called biaccessible if two parameter rays land at $z$. In both cases, we say that the external angles of these two rays are biaccessible as well. In this paper we give upper and lower bounds for the Hausdorff dimension of biaccessible external angles of quadratic polynomials, both in the dynamical and parameter space. In particular, explicitly describe those quadratic polynomials where this dimension equals 1 (if and only if the Julia set is an interval), and when it equals 0, namely, at finite direct bifurcations from the polynomial $z^2$, as well as limit points thereof.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-24T20:21:25.000Z",
      "comment": "28 pages, 3 figures. General update of the main text. H\\\"older continuity of biaccessibility dimension moved to separate paper (where it belongs)",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2019-11-08T14:40:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E15",
      "37F10",
      "37F20",
      "37B10",
      "37B40"
    ],
    "keywords": [
      "quadratic polynomials",
      "hausdorff dimension",
      "biaccessible angles",
      "external angles",
      "julia set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.2544B"
    }
  }
}