{
  "id": "1103.3255",
  "version": "v1",
  "published": "2011-03-16T18:51:45.000Z",
  "updated": "2011-03-16T18:51:45.000Z",
  "title": "Fragile cycles",
  "authors": [
    "Christian Bonatti",
    "Lorenzo J. Diaz"
  ],
  "comment": "25 pages, 13 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study diffeomorphisms $f$ with heterodimensional cycles, that is, heteroclinic cycles associated to saddles $p$ and $q$ with different indices. Such a cycle is called fragile if there is no diffeomorphism close to $f$ with a robust cycle associated to hyperbolic sets containing the continuations of $p$ and $q$. We construct a codimension one submanifold of $\\Difr(\\SS^2\\times \\SS^1)$, $r\\ge 1$, that consists of diffeomorphisms with fragile heterodimensional cycles. Our construction holds for any manifold of dimension $\\ge 4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-16T18:51:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C29",
      "37D20",
      "37D30"
    ],
    "keywords": [
      "fragile cycles",
      "study diffeomorphisms",
      "diffeomorphism close",
      "robust cycle",
      "fragile heterodimensional cycles"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2011.12.002",
      "journal": "Journal of Differential Equations",
      "year": 2012,
      "volume": 252,
      "number": 7,
      "pages": 4176
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JDE...252.4176B"
    }
  }
}