{
  "id": "0712.1455",
  "version": "v2",
  "published": "2007-12-10T12:17:34.000Z",
  "updated": "2009-05-27T15:11:37.000Z",
  "title": "On contact equivalence of systems of ordinary differential equations",
  "authors": [
    "Wojciech Kryński"
  ],
  "categories": [
    "math.CA",
    "math.DG"
  ],
  "abstract": "We consider a problem of equivalence of generic pairs $(X,V)$ on a manifold $M$, where $V$ is a distribution of rank $m$ and $X$ is a distribution of rank one. We construct a canonical bundle with a canonical frame. We prove that two pairs are equivalent if and only if the corresponding frames are diffeomorphic. As a particular case, with $V$ integrable, we provide a new solution to the problem of contact equivalence of systems of $m$ ordinary differential equations: $x^{(k+1)}=F(t,x,x',...,x^{(k)})$, where $k>2$ or $k=2$ and $m>1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-27T15:11:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A55",
      "34A26"
    ],
    "keywords": [
      "ordinary differential equations",
      "contact equivalence",
      "generic pairs",
      "distribution",
      "canonical bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.1455K"
    }
  }
}