{
  "id": "2010.12187",
  "version": "v1",
  "published": "2020-10-23T06:31:42.000Z",
  "updated": "2020-10-23T06:31:42.000Z",
  "title": "Morse index and Maslov-type index of the discrete Hamiltonian system",
  "authors": [
    "Gaosheng Zhu"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we give the definition of Maslov-type index of the discrete Hamiltonian system, and obtain the relation of Morse index and Maslov-type index of the discrete Hamiltonian system which is a generalization of case $\\omega=1$ in \\cite{RoS1}, \\cite{RoS2} and \\cite{Maz1} to case $\\omega \\in {\\bf U}$ via direct method which is different from that of \\cite{RoS1}, \\cite{RoS2} and \\cite{Maz1}. Moreover well-posedness of the splitting numbers $S_{\\omega}$ of the discrete Hamiltonian system is proven, thus index iteration theory in \\cite{Bot1} and \\cite{Lon4} is also valid for the discrete Hamiltonian system case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-23T06:31:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maslov-type index",
      "morse index",
      "discrete hamiltonian system case",
      "index iteration theory",
      "direct method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}