{
  "id": "1709.06717",
  "version": "v1",
  "published": "2017-09-20T03:53:14.000Z",
  "updated": "2017-09-20T03:53:14.000Z",
  "title": "On the growth rate of periodic orbits for vector fields",
  "authors": [
    "Wanlou Wu",
    "Dawei Yang",
    "Yong Zhang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We establish the relationship between the growth rate of periodic orbits and the topological entropy for $C^1$ generic vector fields: this extends a classical result of Katok for $C^{1+\\alpha}(\\alpha>0)$ surface diffeomorphisms to $C^1$ generic vector fields of any dimension. The main difficulty comes from the existence of singularities and the shear of the flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-20T03:53:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic orbits",
      "growth rate",
      "generic vector fields",
      "main difficulty comes",
      "surface diffeomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}