{
  "id": "1710.05802",
  "version": "v1",
  "published": "2017-10-16T16:08:17.000Z",
  "updated": "2017-10-16T16:08:17.000Z",
  "title": "Linking combinatorial and classical dynamics: Conley index and Morse decompositions",
  "authors": [
    "Bogdan Batko",
    "Tomasz Kaczynski",
    "Marian Mrozek",
    "Thomas Wanner"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system F on the geometric realization of the simplicial complex. Moreover, F may be chosen in such a way that the isolated invariant sets, Conley indices, Morse decompositions, and Conley-Morse graphs of the two dynamical systems are in one-to-one correspondence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-16T16:08:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B30",
      "37E15",
      "57M99",
      "57Q05",
      "57Q15"
    ],
    "keywords": [
      "conley index",
      "morse decompositions",
      "linking combinatorial",
      "classical dynamics",
      "simplicial complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}