{
  "id": "1903.05883",
  "version": "v1",
  "published": "2019-03-14T09:51:47.000Z",
  "updated": "2019-03-14T09:51:47.000Z",
  "title": "Symmetries of vector fields: the diffeomorphism centralizer",
  "authors": [
    "Davi Obata"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we study the diffeomorphism centralizer of a vector field: given a vector field it is the set of diffeomorphisms that commutes with the flow. Our main theorem states that for a $C^1$-generic diffeomorphism having at most finitely many sinks or sources, the diffeomorphism centralizer is quasi-trivial. In certain cases, we can promote the quasi-triviality to triviality. We also obtain a criterion for a diffeomorphism in the centralizer to be a reparametrization of the flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-14T09:51:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C10",
      "37C20",
      "37C80",
      "37D30"
    ],
    "keywords": [
      "diffeomorphism centralizer",
      "vector field",
      "symmetries",
      "main theorem states",
      "generic diffeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}