{
  "id": "math/0502235",
  "version": "v2",
  "published": "2005-02-11T10:21:47.000Z",
  "updated": "2007-05-10T13:28:34.000Z",
  "title": "The boundary of hyperbolicity for Henon-like families",
  "authors": [
    "Yongluo Cao",
    "Stefano Luzzatto",
    "Isabel Rios"
  ],
  "comment": "32 pages, 11 figures. Several minor revisions, additional figures, clarifications of some arguments",
  "journal": "Ergodic Theory and Dynamical Systems 28 (2008), no. 4, 1049-1080",
  "doi": "10.1017/S0143385707000776",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider C^{2} Henon-like families of diffeomorphisms of R^{2} and study the boundary of the region of parameter values for which the nonwandering set is uniformly hyperbolic. Assuming sufficient dissipativity, we show that the loss of hyperbolicity is caused by a first homoclinic or heteroclinic tangency and that uniform hyperbolicity estimates hold uniformly in the parameter up to this bifurcation parameter and even, to some extent, at the bifurcation parameter.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-05-10T13:28:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20",
      "37D25"
    ],
    "keywords": [
      "henon-like families",
      "bifurcation parameter",
      "uniform hyperbolicity estimates hold",
      "heteroclinic tangency",
      "first homoclinic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}