{
  "id": "1003.0629",
  "version": "v1",
  "published": "2010-03-02T16:56:42.000Z",
  "updated": "2010-03-02T16:56:42.000Z",
  "title": "On the reduction of the degree of linear differential operators",
  "authors": [
    "Marcin Bobieński",
    "Lubomir Gavrilov"
  ],
  "journal": "Nonlinearity 24 (2011) 373-388",
  "categories": [
    "math.CA",
    "math.DS"
  ],
  "abstract": "Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-02T16:56:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C08",
      "34M03",
      "34M35"
    ],
    "keywords": [
      "linear differential operator",
      "plane polynomial vector fields",
      "differential field",
      "minimal degree",
      "picard-fuchs equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/24/2/002",
      "journal": "Nonlinearity",
      "year": 2011,
      "month": "Feb",
      "volume": 24,
      "number": 2,
      "pages": 373
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011Nonli..24..373B"
    }
  }
}