{
  "id": "math/9909091",
  "version": "v1",
  "published": "1999-09-16T11:07:46.000Z",
  "updated": "1999-09-16T11:07:46.000Z",
  "title": "Isochronicity and Commutation of Polynomial Vector Fields",
  "authors": [
    "E. P. Volokitin",
    "V. V. Ivanov"
  ],
  "comment": "21 pages, LaTeX, 5 PostScript Figures",
  "journal": "Siberian Mathematical Journal, Vol.40, No.1, p.22-37",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study a connection between the isochronicity of a center of a polynomial vector field and the existence of a polynomial commuting system. We demonstrate an isochronous system of degree 4 which does not commute with any polynomial system. We prove that among the Newton polynomial systems only the Lienard and Abel systems may commute with transversal polynomial fields. We give a full and constructive description of centralizers of the Abel polynomial systems. We give new examples of isochronous systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-09-16T11:07:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C05"
    ],
    "keywords": [
      "polynomial vector field",
      "isochronicity",
      "commutation",
      "transversal polynomial fields",
      "isochronous system"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......9091V"
    }
  }
}