{
  "id": "math/0503363",
  "version": "v1",
  "published": "2005-03-17T17:37:37.000Z",
  "updated": "2005-03-17T17:37:37.000Z",
  "title": "The Ten Martini Problem",
  "authors": [
    "Artur Avila",
    "Svetlana Jitomirskaya"
  ],
  "comment": "31 pages, no figures",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We prove the conjecture (known as the ``Ten Martini Problem'' after Kac and Simon) that the spectrum of the almost Mathieu operator is a Cantor set for all non-zero values of the coupling and all irrational frequencies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-17T17:37:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "martini problem",
      "mathieu operator",
      "cantor set",
      "non-zero values"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/3-540-34273-7_2",
      "journal": "Lecture Notes in Physics, Berlin Springer Verlag",
      "year": 2006,
      "volume": 690,
      "pages": 5
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006LNP...690....5A"
    }
  }
}