{
  "id": "1803.04800",
  "version": "v1",
  "published": "2018-03-13T13:43:02.000Z",
  "updated": "2018-03-13T13:43:02.000Z",
  "title": "Convergence versus integrability in normal form, III",
  "authors": [
    "Nguyen Tien Zung"
  ],
  "comment": "1st version, 12 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In two previous papers we showed that any analytically integrable vector field admits a local analytic Poincar\\'e-Birkhoff normalization in the neighborhood of a singular point. The aim of this paper is to extend this normalization result to the case when the vector field is only integrable in the sense of Darboux: the first integrals are of Darboux type and not necessarily analytic, and the commuting vector fields are meromorphic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-13T13:43:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normal form",
      "local analytic poincare-birkhoff normalization",
      "convergence",
      "integrability",
      "analytically integrable vector field admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}