{
  "id": "math/9201282",
  "version": "v1",
  "published": "1991-04-12T00:00:00.000Z",
  "updated": "1991-04-12T00:00:00.000Z",
  "title": "The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets",
  "authors": [
    "Mitsuhiro Shishikura"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "It is shown that the boundary of the Mandelbrot set $M$ has Hausdorff dimension two and that for a generic $c \\in \\bM$, the Julia set of $z \\mapsto z^2+c$ also has Hausdorff dimension two. The proof is based on the study of the bifurcation of parabolic periodic points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1991-04-12T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hausdorff dimension",
      "julia set",
      "mandelbrot set",
      "parabolic periodic points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}