{
  "id": "2310.03099",
  "version": "v1",
  "published": "2023-10-04T18:28:25.000Z",
  "updated": "2023-10-04T18:28:25.000Z",
  "title": "Conley index for multivalued maps on finite topological spaces",
  "authors": [
    "Jonathan Barmak",
    "Marian Mrozek",
    "Thomas Wanner"
  ],
  "categories": [
    "math.DS",
    "math.AT"
  ],
  "abstract": "We develop Conley's theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map which satisfies appropriate regularity conditions, we establish the notions of isolated invariant sets and index pairs, and use them to introduce a well-defined Conley index. In addition, we verify some of its fundamental properties such as the Wazewski property and continuation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-04T18:28:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B30",
      "37E15",
      "57M99",
      "57Q05",
      "57Q15"
    ],
    "keywords": [
      "finite topological spaces",
      "multivalued map",
      "satisfies appropriate regularity conditions",
      "conleys theory",
      "isolated invariant sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}