{
  "id": "2404.07233",
  "version": "v1",
  "published": "2024-04-04T20:01:32.000Z",
  "updated": "2024-04-04T20:01:32.000Z",
  "title": "Structure of the codimesion one gradient flows with at most six singular points on the Möbius strip",
  "authors": [
    "Maria Loseva",
    "Alexandr Prishlyak",
    "Kateryna Semenovych",
    "Yuliia Volianiuk"
  ],
  "comment": "14 pages, 14 figures. arXiv admin note: substantial text overlap with arXiv:2303.14975",
  "categories": [
    "math.DS"
  ],
  "abstract": "We describe all possible topological structures of Morse flows and typical one-parametric gradient bifurcation on the M\\\"obius strip in the case that the number of singular point of flows is at most six. To describe structures, we use the separatrix diagrams of flows. The saddle-node bifurcation is specified by selecting a separatrix in the diagram of the Morse flow befor the bifurcation and the saddle connection is specified by a separatrix, which connect two saddles on the diagram.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-04T20:01:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "G.1.7"
    ],
    "keywords": [
      "singular point",
      "gradient flows",
      "möbius strip",
      "codimesion",
      "morse flow befor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}