{
  "id": "0804.0306",
  "version": "v2",
  "published": "2008-04-02T08:12:20.000Z",
  "updated": "2008-04-03T17:26:18.000Z",
  "title": "On the obstruction to linearizability of 2-order ordinary differential equations",
  "authors": [
    "Valeriy A. Yumaguzhin"
  ],
  "comment": "14 pages; Ams-LateX 2e",
  "journal": "Acta Applicandae Mathematicae, Vol. 83, No. 1-2, 2004. pp.133-148",
  "categories": [
    "math.DG",
    "math.CA"
  ],
  "abstract": "In this paper, we investigate the action of pseudogroup of all point transformations on the natural bundle of equations $y'' = u^0(x,y) + u^1(x,y)y' + u^2(x,y)(y')^2 + u^3(x,y)(y')^3$. We calculate the 1-st nontrivial differential invariant of this action. It is a horizontal differential 2-form with values in some algebra, it is defined on the bundle of 2--jets of sections of the considered bundle. We prove that this form is a unique obstruction to linearizability of these equations by point transformations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-03T17:26:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A55",
      "53C10",
      "53C15",
      "34A30",
      "34A26",
      "34C20",
      "58F35"
    ],
    "keywords": [
      "ordinary differential equations",
      "linearizability",
      "point transformations",
      "nontrivial differential invariant",
      "unique obstruction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.0306Y"
    }
  }
}