{
  "id": "1512.01280",
  "version": "v1",
  "published": "2015-12-03T23:24:08.000Z",
  "updated": "2015-12-03T23:24:08.000Z",
  "title": "Existence of Heterodimensional Cycles near Shilnikov Loops",
  "authors": [
    "Dongchen Li",
    "Dmitry V. Turaev"
  ],
  "comment": "29pages, 6 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that a pair of heterodimensional cycles can be born at the bifurcations of a pair of Shilnikov loops (i.e. homoclinic loops to a saddle-focus) of a volume-hyperbolic system with a $\\mathbb{Z}_2$ symmetry. We also show that the heterodimensional cycles can belong to a chain-transitive attractor of the system along with persistent homoclinic tangency.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-03T23:24:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37G20",
      "37G25",
      "37G35"
    ],
    "keywords": [
      "heterodimensional cycles",
      "shilnikov loops",
      "persistent homoclinic tangency",
      "homoclinic loops",
      "volume-hyperbolic system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}