{
  "id": "math/0204266",
  "version": "v1",
  "published": "2002-04-22T13:07:26.000Z",
  "updated": "2002-04-22T13:07:26.000Z",
  "title": "Random perturbations of codimension one homoclinic tangencies in dimension 3",
  "authors": [
    "Vitor Araujo"
  ],
  "comment": "22 pages; 5 figures",
  "journal": "Dynamical Systems, An International Journal, Vol. 18, No. 1 (2003), 35-55.",
  "categories": [
    "math.DS"
  ],
  "abstract": "Adding small random parametric noise to an arc of diffeomophisms of a manifold of dimension 3, generically unfolding a codimension one quadratic homoclinic tangency q associated to a sectionally dissipative saddle fixed point p, we obtain not more than a finite number of physical probability measures, whose ergodic basins cover the orbits which are recurrent to a neighborhood of the tangency point $q$. This result is in contrast to the extension of Newhouse's phenomenon of coexistence of infinitely many sinks obtained by Palis and Viana in this setting. There is a similar result for the simpler bidimensional case whose proof relies on geometric arguments. We now extend the arguments to cover three dimensional manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-04-22T13:07:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random perturbations",
      "dissipative saddle fixed point",
      "codimension",
      "adding small random parametric noise",
      "simpler bidimensional case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......4266A"
    }
  }
}