{
  "id": "2012.01808",
  "version": "v1",
  "published": "2020-12-03T10:25:19.000Z",
  "updated": "2020-12-03T10:25:19.000Z",
  "title": "Counting periodic orbits of vector fields over smooth closed manifolds",
  "authors": [
    "Eaman Eftekhary"
  ],
  "categories": [
    "math.DS",
    "math.DG",
    "math.GT"
  ],
  "abstract": "We address the problem of counting periodic orbits of vector fields on smooth closed manifolds. The space of non-constant periodic orbits is enlarged to a complete space by adding the ghost orbits, which are decorations of the zeros of vector fields. Associated with any compact and open subset $\\Gamma$ of the moduli space of periodic and ghost orbits, we define an integer weight. When the vector field moves along a path, and $\\Gamma$ deforms in a compact and open family, we show that the weight function stays constant. We also give a number of examples and computations, which illustrate the applications of our main theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-03T10:25:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C10"
    ],
    "keywords": [
      "counting periodic orbits",
      "smooth closed manifolds",
      "ghost orbits",
      "weight function stays constant",
      "non-constant periodic orbits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}