{
  "id": "math/0105193",
  "version": "v2",
  "published": "2001-05-23T17:37:07.000Z",
  "updated": "2002-03-13T19:26:36.000Z",
  "title": "Convergence versus integrability in Poincare-Dulac normal form",
  "authors": [
    "Nguyen Tien Zung"
  ],
  "comment": "2nd version, substantial revision, new title",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that, to find a Poincare-Dulac normalization for a vector field is the same as to find and linearize a torus action which preserves the vector field. Using this toric characterization and other geometrical arguments, we prove that any local analytic vector field which is integrable in the non-Hamiltonian sense admits a local convergent Poincare-Dulac normalization. These results generalize the main results of our previous paper from the Hamiltonian case to the non-Hamiltonian case. Similar results are presented for the case of isochore vector fields.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-03-13T19:26:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37G05",
      "70K45",
      "34C14"
    ],
    "keywords": [
      "poincare-dulac normal form",
      "convergence",
      "local convergent poincare-dulac normalization",
      "integrability",
      "local analytic vector field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......5193T"
    }
  }
}