{
  "id": "1903.01933",
  "version": "v1",
  "published": "2019-03-05T17:04:13.000Z",
  "updated": "2019-03-05T17:04:13.000Z",
  "title": "Sparkling saddle loops of vector fields on surfaces",
  "authors": [
    "Ivan Shilin"
  ],
  "comment": "23 pages, 2 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "An orientation-preserving non-contractible separatrix loop of a hyperbolic saddle of a vector field on a two-dimensional surface may be accumulated by a separatrix of the same saddle. We study the unfolding of such loops in generic one-parameter families of vector fields as a semi-local bifurcation. As a byproduct, we construct a countable family of pairwise non-equivalent germs of bifurcation diagrams that appear in locally generic one-parameter families.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-05T17:04:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vector field",
      "sparkling saddle loops",
      "locally generic one-parameter families",
      "hyperbolic saddle",
      "orientation-preserving non-contractible separatrix loop"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}