{
  "id": "1808.10408",
  "version": "v1",
  "published": "2018-08-30T17:27:48.000Z",
  "updated": "2018-08-30T17:27:48.000Z",
  "title": "On the inhomogeneity of the Mandelbrot set",
  "authors": [
    "Yusheng Luo"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We will show the Mandelbrot set $M$ is locally conformally inhomogeneous: the only conformal map $f$ defined in an open set $U$ intersecting $\\partial M$ and satisfying $f(U\\cap\\partial M)\\subset \\partial M$ is the identity map. The proof uses the study of local conformal symmetries of the Julia sets of polynomials: we will show in many cases, the dynamics can be recovered from the local conformal structure of the Julia sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-30T17:27:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mandelbrot set",
      "inhomogeneity",
      "julia sets",
      "local conformal structure",
      "local conformal symmetries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}