{
  "id": "1104.2979",
  "version": "v2",
  "published": "2011-04-15T08:22:21.000Z",
  "updated": "2011-07-22T12:32:35.000Z",
  "title": "There is only one KAM curve",
  "authors": [
    "Carlo Carminati",
    "Stefano Marmi",
    "David Sauzin"
  ],
  "comment": "33 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the standard family of area-preserving twist maps of the annulus and the corresponding KAM curves. Addressing a question raised by Kolmogorov, we show that, instead of viewing these invariant curves as separate objects, each of which having its own Diophantine frequency, one can encode them in a single function of the frequency which is naturally defined in a complex domain containing the real Diophantine frequencies and which is monogenic in the sense of Borel; this implies a remarkable property of quasianalyticity, a form of uniqueness of the monogenic continuation, although real frequencies constitute a natural boundary for the analytic continuation from the Weierstrass point of view because of the density of the resonances.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-22T12:32:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diophantine frequency",
      "real diophantine frequencies",
      "real frequencies constitute",
      "area-preserving twist maps",
      "single function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.2979C"
    }
  }
}