{
  "id": "math/0105222",
  "version": "v1",
  "published": "2001-05-27T18:21:42.000Z",
  "updated": "2001-05-27T18:21:42.000Z",
  "title": "Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic family",
  "authors": [
    "Artur Avila",
    "Carlos Gustavo Moreira"
  ],
  "comment": "34 pages, no figures, first version",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider quasisymmetric reparametrizations of the parameter space of the quadratic family. We prove that the set of quadratic maps which are either regular or Collet-Eckmann with polynomial recurrence of the critical orbit has full Lebesgue measure. (The intent of this work is just to be a rigorous reference for the companion preprint Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative. It is based on the LaTeX file of the paper Statistical properties of unimodal maps: the quadratic family. The proofs are very similar and in many places differ just by change of constants.)",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-05-27T18:21:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic family",
      "collet-eckmann condition",
      "quasisymmetric robustness",
      "unimodal maps",
      "full lebesgue measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......5222A"
    }
  }
}