{
  "id": "2102.05175",
  "version": "v1",
  "published": "2021-02-09T23:07:06.000Z",
  "updated": "2021-02-09T23:07:06.000Z",
  "title": "Transition space for the continuity of the Lyapunov exponent of quasiperiodic Schrödinger cocycles",
  "authors": [
    "Lingrui Ge",
    "Yiqian Wang",
    "Jiangong You",
    "Xin Zhao"
  ],
  "comment": "27 pages",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We construct discontinuous point of the Lyapunov exponent of quasiperiodic Schr\\\"odinger cocycles in the Gevrey space $G^{s}$ with $s>2$. In contrast, the Lyapunov exponent has been proved to be continuous in the Gevrey space $G^{s}$ with $s<2$ \\cite{klein,cgyz}. This shows that $G^2$ is the transition space for the continuity of the Lyapunov exponent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-09T23:07:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lyapunov exponent",
      "quasiperiodic schrödinger cocycles",
      "transition space",
      "continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}