{
  "id": "math/0508302",
  "version": "v3",
  "published": "2005-08-16T19:09:18.000Z",
  "updated": "2005-10-07T16:30:43.000Z",
  "title": "Computable conditions for the occurrence of non-uniform hyperbolicity in families of one-dimensional maps",
  "authors": [
    "Stefano Luzzatto",
    "Hiroki Takahasi"
  ],
  "comment": "44 pages",
  "journal": "Nonlinearity 19 (2006) no. 7, 1657-1695",
  "doi": "10.1088/0951-7715/19/7/013",
  "categories": [
    "math.DS",
    "math.NA"
  ],
  "abstract": "We formulate and prove a Jakobson-Benedicks-Carleson type theorem on the occurence of nonuniform hyperbolicity (stochastic dynamics) in families of one-dimensional maps, based on \"computable starting conditions\" and providing \"explicit, computable,\" lower bounds for the measure of the set of selected parameters. As a first application of our results we show that the set of parameters corresponding to maps in the quadratic family f_{a}(x) = x^{2}-a which have an absolutely continuous invariant probability measure is at least 10^-5000 !",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-10-07T16:30:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37M99",
      "37E25"
    ],
    "keywords": [
      "one-dimensional maps",
      "non-uniform hyperbolicity",
      "computable conditions",
      "occurrence",
      "absolutely continuous invariant probability measure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}