{
  "id": "1306.2736",
  "version": "v1",
  "published": "2013-06-12T07:52:38.000Z",
  "updated": "2013-06-12T07:52:38.000Z",
  "title": "Quadratic polynomials, multipliers and equidistribution",
  "authors": [
    "Xavier Buff",
    "Thomas Gauthier"
  ],
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Given a sequence of complex numbers {\\rho}_n, we study the asymptotic distribution of the sets of parameters c {\\epsilon} C such that the quadratic maps z^2 +c has a cycle of period n and multiplier {\\rho}_n. Assume 1/n.log|{\\rho}_n| tends to L. If L {\\leq} log 2, they equidistribute on the boundary of the Mandelbrot set. If L > log 2 they equidistribute on the equipotential of the Mandelbrot set of level 2L - 2 log 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-12T07:52:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic polynomials",
      "multiplier",
      "equidistribution",
      "mandelbrot set",
      "asymptotic distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.2736B"
    }
  }
}