{
  "id": "math/9911188",
  "version": "v1",
  "published": "1999-11-23T21:26:17.000Z",
  "updated": "1999-11-23T21:26:17.000Z",
  "title": "On $C^r-$closing for flows on 2-manifolds",
  "authors": [
    "Carlos Gutierrez"
  ],
  "comment": "7 pages, 1 figure",
  "doi": "10.1088/0951-7715/13/6/301",
  "categories": [
    "math.DS"
  ],
  "abstract": "For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a $C^r$, $1\\le r\\le \\infty$, vector field, with finitely many singularities, on a compact orientable surface M. Given a nontrivial recurrent point $p\\in M$ of X, the holonomy map around p is semi-conjugate to an iet $E :[0,1) \\to [0,1).$ If $E\\in B$ then there exists a $C^r$ vector field Y, arbitrarily close to X, in the $C^r-$topology, such that Y has a closed trajectory passing through p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-11-23T21:26:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58F10",
      "58F11",
      "58F18",
      "58F25"
    ],
    "keywords": [
      "vector field",
      "full measure subset",
      "interval exchange transformations",
      "nontrivial recurrent point",
      "compact orientable surface"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}