{
  "id": "math/0702011",
  "version": "v1",
  "published": "2007-02-01T08:24:09.000Z",
  "updated": "2007-02-01T08:24:09.000Z",
  "title": "Multipliers of periodic orbits of quadratic polynomials and the parameter plane",
  "authors": [
    "Genadi Levin"
  ],
  "comment": "28 pages, no figures",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We prove an extension results for the multiplier of an attracting periodic orbit of a quadratic map as a function of the parameter. This has applications to the problem of geometry of the Mandelbrot and Julia sets. In particular, we prove that the size of p/q-limb of a hyperbolic component of the Mandelbrot set of period n is O(4^n/p), and give an explicit condition on internal arguments under which the Julia set of corresponding (unique) infinitely renormalizable quadratic polynomial is not locally connected",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-01T08:24:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F45"
    ],
    "keywords": [
      "parameter plane",
      "multiplier",
      "julia set",
      "quadratic map",
      "infinitely renormalizable quadratic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2011L"
    }
  }
}