{
  "id": "1903.00062",
  "version": "v1",
  "published": "2019-02-28T20:38:24.000Z",
  "updated": "2019-02-28T20:38:24.000Z",
  "title": "Equidistribution of critical points of the multipliers in the quadratic family",
  "authors": [
    "Tanya Firsova",
    "Igors Gorbovickis"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "A parameter $c_0\\in\\mathbb C$ in the family of quadratic polynomials $f_c(z)=z^2+c$ is a critical point of a period $n$ multiplier, if the map $f_{c_0}$ has a periodic orbit of period $n$, whose multiplier, viewed as a locally analytic function of $c$, has a vanishing derivative at $c=c_0$. We prove that all critical points of period $n$ multipliers equidistribute on the boundary of the Mandelbrot set, as $n\\to\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-28T20:38:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical point",
      "quadratic family",
      "equidistribution",
      "quadratic polynomials",
      "periodic orbit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}