{
  "id": "math/0312279",
  "version": "v1",
  "published": "2003-12-14T15:26:51.000Z",
  "updated": "2003-12-14T15:26:51.000Z",
  "title": "Homeomorphisms of the Mandelbrot Set",
  "authors": [
    "Wolf Jung"
  ],
  "comment": "Preprint of a paper submitted to Dynamics in the Complex Plane, proceedings of a symposium in honour of Bodil Branner, June 19--21 2003, Holbaek",
  "journal": "Dynamics on the Riemann Sphere, A Bodil Branner Festschrift, P. G. Hjorth, C. L. Petersen Eds., EMS January 2006, pp 139-159. ISBN 3-03719-011-6.",
  "categories": [
    "math.DS"
  ],
  "abstract": "On subsets E of the Mandelbrot set M, homeomorphisms are constructed by quasi-conformal surgery. When the dynamics of quadratic polynomials is changed piecewise by a combinatorial construction, a general theorem yields the corresponding homeomorphism h: E to E in the parameter plane. Each h has two fixed points in E, and a countable family of mutually homeomorphic fundamental domains. Possible generalizations to other families of polynomials or rational mappings are discussed. The homeomorphisms on subsets E of M constructed by surgery are extended to homeomorphisms of M, and employed to study groups of non-trivial homeomorphisms h: M to M . It is shown that these groups have the cardinality of the continuum, and they are not compact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-14T15:26:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F45"
    ],
    "keywords": [
      "mandelbrot set",
      "general theorem yields",
      "mutually homeomorphic fundamental domains",
      "quasi-conformal surgery",
      "parameter plane"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12279J"
    }
  }
}