{
  "id": "1410.0101",
  "version": "v1",
  "published": "2014-10-01T03:57:20.000Z",
  "updated": "2014-10-01T03:57:20.000Z",
  "title": "Cantor spectrum for a class of $C^2$ quasiperiodic Schrödinger operators",
  "authors": [
    "Yiqian Wang",
    "Zhenghe Zhang"
  ],
  "comment": "21 pages, preliminary version, all comments are welcome",
  "categories": [
    "math.DS",
    "math.SP"
  ],
  "abstract": "We show that for a class of $C^2$ quasiperiodic potentials and for any Diophantine frequency, the spectrum of the corresponding Schr\\\"odinger operators is Cantor. Our approach is of purely dynamical systems, which depends on a detailed analysis of asymptotic stable and unstable directions. We also apply it to general $\\mathrm{SL}(2,\\mathbb R)$ cocycles, and obtain that uniform hyperbolic systems form a open and dense set in some one-parameter family.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-01T03:57:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20",
      "34L05"
    ],
    "keywords": [
      "quasiperiodic schrödinger operators",
      "cantor spectrum",
      "uniform hyperbolic systems form",
      "dense set",
      "quasiperiodic potentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.0101W"
    }
  }
}