{
  "id": "1604.00431",
  "version": "v1",
  "published": "2016-04-01T23:13:14.000Z",
  "updated": "2016-04-01T23:13:14.000Z",
  "title": "Homoclinic Bifurcations that Give Rise to Heterodimensional Cycles near A Saddle-Focus Equilibrium",
  "authors": [
    "Dongchen Li"
  ],
  "comment": "28 pages, 12 figures. arXiv admin note: substantial text overlap with arXiv:1512.01280",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that heterodimensional cycles can be born at the bifurcations of a pair of homoclinic loops to a saddle-focus equilibrium for flows in dimension 4 and higher. In addition to the classical heterodimensional connection between two periodic orbits, we found two new types of heterodimensional connections: one is a heteroclinic between a periodic orbit of index 2 and a homoclinic loop, and the other connects a periodic orbit of index 3 to the saddle-focus equilibrium.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-01T23:13:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37G20",
      "37G25"
    ],
    "keywords": [
      "saddle-focus equilibrium",
      "heterodimensional cycles",
      "homoclinic bifurcations",
      "periodic orbit",
      "homoclinic loop"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160400431L"
    }
  }
}