{
  "id": "math/0105067",
  "version": "v2",
  "published": "2001-05-09T11:37:38.000Z",
  "updated": "2002-02-13T23:15:33.000Z",
  "title": "Renormalisation scheme for vector fields on T2 with a diophantine frequency",
  "authors": [
    "Joao Lopes-Dias"
  ],
  "comment": "final version",
  "doi": "10.1088/0951-7715/15/3/308",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct a rigorous renormalisation scheme for analytic vector fields on the 2-torus of Poincare type. We show that iterating this procedure there is convergence to a limit set with a ``Gauss map'' dynamics on it, related to the continued fraction expansion of the slope of the frequencies. This is valid for diophantine frequency vectors.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-02-13T23:15:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diophantine frequency vectors",
      "analytic vector fields",
      "rigorous renormalisation scheme",
      "continued fraction expansion",
      "gauss map"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}