{
  "id": "1311.4282",
  "version": "v3",
  "published": "2013-11-18T07:13:52.000Z",
  "updated": "2013-12-26T10:04:21.000Z",
  "title": "Uniform Positivity and Continuity of Lyapunov Exponents for a Class of $C^2$ Quasiperiodic Schrödinger Cocycles ",
  "authors": [
    "Yiqian Wang",
    "Zhenghe Zhang"
  ],
  "comment": "49 pages, 6 figures, a continuity result added",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that for a class of $C^2$ quasiperiodic potentials and for any Diophantine frequency, the Lyapunov exponents of the corresponding Schr\\\"odinger cocycles are uniformly positive and weak H\\\"older continuous as function of energies. As a corollary, we also obtain that the corresponding integrated density of states (IDS) is weak H\\\"older continous. Our approach is of purely dynamical systems, which depends on a detailed analysis of asymptotic stable and unstable directions. We also apply it to more general $\\mathrm{SL}(2,\\mathbb R)$ cocycles, which in turn can be applied to get uniform positivity and continuity of Lyapuonv exponents around unique nondegenerate extremal points of any smooth potential, and to a certain class of $C^2$ Szeg\\H o cocycles.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-12-26T10:04:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "47A10"
    ],
    "keywords": [
      "quasiperiodic schrödinger cocycles",
      "uniform positivity",
      "lyapunov exponents",
      "continuity",
      "unique nondegenerate extremal points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.4282W"
    }
  }
}