{
  "id": "1407.4560",
  "version": "v1",
  "published": "2014-07-17T05:16:23.000Z",
  "updated": "2014-07-17T05:16:23.000Z",
  "title": "Closed Orbits and Integrability for singularities of complex vector fields in dimension three",
  "authors": [
    "Leonardo Câmara",
    "Bruno Scardua"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper is about the integrability of complex vector fields in dimension three in a neighborhood of a singular point. More precisely, we study the existence of holomorphic first integrals for isolated singularities of holomorphic vector fields in complex dimension three, pursuing the discussion started in \\cite{CaSc2009}. Under generic conditions, we prove a topological criteria for the existence of a holomorphic first integral. Our result may be seen as a kind of Reeb stability result for the framework of vector fields singularities in complex dimension three. As a consequence, we prove that, for the class of singularities we consider, the existence of a holomorphic first integral is invariant under topological equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-17T05:16:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F75",
      "57R30",
      "32M25",
      "32S65"
    ],
    "keywords": [
      "complex vector fields",
      "holomorphic first integral",
      "closed orbits",
      "integrability",
      "complex dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.4560C"
    }
  }
}