{
  "annotation_id": "b8f744c6-3f24-4346-bad0-94a5ec1c92e2",
  "date_created": "2026-02-17T05:53:08.498000Z",
  "date_modified": "2026-02-17T05:53:08.498000Z",
  "file_hash": "176435ed0d7d86ca43565cf317a50a6874019ee1c00579d831a9b27d4d4339c9",
  "private": false,
  "record": {
    "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.",
    "arxiv_id": "2601.06926",
    "authors": [
      "Illia Ovtsynov",
      "Alexandr Prishlyak"
    ],
    "categories": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "The structure of Morse flows and co-dimension one gradient flows on the sphere with holes",
    "url": "https://arxiv.org/abs/2601.06926",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "376f529b-d66d-4cae-9c86-76aacffa4a4f",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}