{
  "id": "2404.02223",
  "version": "v1",
  "published": "2024-04-02T18:18:25.000Z",
  "updated": "2024-04-02T18:18:25.000Z",
  "title": "Structure of Morse flows with at most six singular points on the torus with a hole",
  "authors": [
    "Maria Loseva",
    "Alexandr Prishlyak",
    "Kateryna Semenovych",
    "Dariia Synieok"
  ],
  "comment": "9 pages, 5 figures",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "We describe all possible topological structures of Morse flows and typical gradient saddle-nod bifurcation of flows on the 2-dimensional torus with a hole in the case that the number of singular point of flows is at most six. To describe structures, we use separatrix diagrams of flows. The saddle-node bifurcation is specified by selecting a separatrix in the separatrix diagram of the flow befor the bifurcation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-02T18:18:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "G.1.7"
    ],
    "keywords": [
      "singular point",
      "morse flows",
      "separatrix diagram",
      "typical gradient saddle-nod bifurcation",
      "flow befor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}