{
  "id": "1206.3005",
  "version": "v1",
  "published": "2012-06-14T05:06:45.000Z",
  "updated": "2012-06-14T05:06:45.000Z",
  "title": "A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers",
  "authors": [
    "Jaume Llibre",
    "Daniel Peralta-Salas"
  ],
  "journal": "SIGMA 8 (2012), 035, 9 pages",
  "doi": "10.3842/SIGMA.2012.035",
  "categories": [
    "math.DS",
    "math.CA",
    "nlin.SI"
  ],
  "abstract": "We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields which are volume preserving and possess nontrivial normalizers. Our approach is geometric and coordinate-free and hence it works on any smooth orientable manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-14T05:06:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vector fields",
      "integrating factor",
      "explicit first integrals",
      "possess nontrivial normalizers",
      "smooth orientable manifold"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2012,
      "month": "Jun",
      "volume": 8,
      "pages": "035"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012SIGMA...8..035L"
    }
  }
}