{
  "id": "1008.5355",
  "version": "v1",
  "published": "2010-08-31T16:27:41.000Z",
  "updated": "2010-08-31T16:27:41.000Z",
  "title": "Homeomorphisms between limbs of the Mandelbrot set",
  "authors": [
    "Dzmitry Dudko",
    "Dierk Schleicher"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that for every hyperbolic component of the Mandelbrot set, any two limbs with equal denominators are homeomorphic so that the homeomorphism preserves periods of hyperbolic components. This settles a conjecture on the Mandelbrot set that goes back to 1994.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-31T16:27:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mandelbrot set",
      "hyperbolic component",
      "homeomorphism preserves periods",
      "equal denominators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.5355D"
    }
  }
}