{
  "id": "2303.14975",
  "version": "v1",
  "published": "2023-03-27T08:12:50.000Z",
  "updated": "2023-03-27T08:12:50.000Z",
  "title": "Typical one-parameter bifurcations of gradient flows with at most six singular points on the 2-sphere with holes",
  "authors": [
    "Svitlana Bilun",
    "Maria Loseva",
    "Olena Myshnova",
    "Alexandr Prishlyak"
  ],
  "comment": "17 pages, 19 figures. arXiv admin note: text overlap with arXiv:2303.10929",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "We describe all possible topological structures of typical one-parameter bifurcations of gradient flows on the 2-sphere with holes in the case that the number of singular point of flows is at most six. To describe structures, we separatrix diagrams of flows. The saddle-node singularity is specified by selecting a separatrix in the diagram of the flow befor the bifurcation and the saddle connection is specified by a separatrix, which conect two saddles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-27T08:12:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "G.1.7"
    ],
    "keywords": [
      "typical one-parameter bifurcations",
      "singular point",
      "gradient flows",
      "separatrix diagrams",
      "saddle-node singularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}