{
  "id": "0811.1173",
  "version": "v1",
  "published": "2008-11-07T16:26:16.000Z",
  "updated": "2008-11-07T16:26:16.000Z",
  "title": "On the centralizer of diffeomorphisms of the half-line",
  "authors": [
    "Hélène Eynard"
  ],
  "comment": "16 pages, 5 figures",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "Let f be a smooth diffeomorphism of the half-line fixing only the origin and Z^r its centralizer in the group of C^r diffeomorphisms. According to well-known results of Szekeres and Kopell, Z^1 is a one-parameter group. On the other hand, Sergeraert constructed an f whose centralizer Z^r, $2\\le r\\le \\infty$, reduces to the group generated by f. We show that Z^r can actually be a proper dense and uncountable subgroup of Z^1 and that this phenomenon is not scarce.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-07T16:26:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05",
      "57R50"
    ],
    "keywords": [
      "centralizer",
      "smooth diffeomorphism",
      "well-known results",
      "one-parameter group",
      "proper dense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.1173E"
    }
  }
}