{
  "id": "1506.06797",
  "version": "v1",
  "published": "2015-06-22T21:38:34.000Z",
  "updated": "2015-06-22T21:38:34.000Z",
  "title": "An open set of structurally unstable families of vector fields in the two-sphere",
  "authors": [
    "Yulij Ilyashenko",
    "Yury Kudryashov",
    "Ilya Schurov"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "This is the first part of a two parts paper dedicated to global bifurcations in the plane. In this part we construct an open set of three parameter families whose topological classification has a numerical invariant that may take an arbitrary positive value. In the second part we construct an open set of six parameter families whose topological classification has a functional invariant. Any germ of a monotonically increasing function $(\\mathbb R, a) \\to (\\mathbb R,b)$ for any $a > 0$, $b > 0$ may be realized as this invariant. Here \"families\" are \"families of vector fields in the two-sphere\".",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-22T21:38:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open set",
      "structurally unstable families",
      "vector fields",
      "two-sphere",
      "parameter families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}