{
  "id": "1104.0980",
  "version": "v1",
  "published": "2011-04-06T00:38:15.000Z",
  "updated": "2011-04-06T00:38:15.000Z",
  "title": "Stabilization of heterodimensional cycles",
  "authors": [
    "Christian Bonatti",
    "Lorenzo J. Diaz",
    "Shin Kiriki"
  ],
  "comment": "31 pages, 9 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider diffeomorphisms $f$ with heteroclinic cycles associated to saddles $P$ and $Q$ of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to $f$ with a robust cycle associated to hyperbolic sets containing the continuations of $P$ and $Q$. We focus on the case where the indices of these two saddles differ by one. We prove that, excluding one particular case (so-called twisted cycles that additionally satisfy some geometrical restrictions), all such cycles can be stabilized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-06T00:38:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C29",
      "37D20",
      "37D30"
    ],
    "keywords": [
      "heterodimensional cycles",
      "stabilization",
      "diffeomorphisms close",
      "robust cycle",
      "saddles differ"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/25/4/931",
      "journal": "Nonlinearity",
      "year": 2012,
      "month": "Apr",
      "volume": 25,
      "number": 4,
      "pages": 931
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012Nonli..25..931B"
    }
  }
}