{
  "id": "math/0401202",
  "version": "v1",
  "published": "2004-01-16T14:51:55.000Z",
  "updated": "2004-01-16T14:51:55.000Z",
  "title": "On the integrability of the n-centre problem",
  "authors": [
    "Andreas Knauf",
    "Iskander A. Taimanov"
  ],
  "comment": "22 pages, a short announcement see in math.DS/0312429",
  "journal": "Mathematische Annalen 331 (2005), 631--649",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is known that for $n \\geq 3$ centres and positive energies the $n$-centre problem of celestial mechanics leads to a flow with a strange repellor and positive topological entropy. Here we consider the energies above some threshold and show: Whereas for arbitrary $g >1$ independent integrals of Gevrey class $g$ exist, no real-analytic (that is, Gevrey class 1) independent integral exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-16T14:51:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "n-centre problem",
      "integrability",
      "independent integral",
      "gevrey class",
      "celestial mechanics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1202K"
    }
  }
}