{
  "id": "1501.05380",
  "version": "v1",
  "published": "2015-01-22T03:19:51.000Z",
  "updated": "2015-01-22T03:19:51.000Z",
  "title": "Quasi-Periodic Schrödinger Cocycles with Positive Lyapunov Exponent are not Open in the Smooth Topology",
  "authors": [
    "Yiqian Wang",
    "Jiangong You"
  ],
  "comment": "45 pages, 3 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "One knows that the set of quasi-periodic Schr\\\"odinger cocycles with positive Lyapunov exponent is open and dense in the analytic topology. In this paper, we construct cocycles with positive Lyapunov exponent which can be approximated by ones with zero Lyapunov exponent in the space of ${\\cal C}^ l$ ($1 \\le l\\le \\infty$) smooth quasi-periodic cocycles. As a consequence, the set of quasi-periodic Schr\\\"odinger cocycles with positive Lyapunov exponent is not ${\\cal C}^ l$ open.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-22T03:19:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25"
    ],
    "keywords": [
      "positive lyapunov exponent",
      "quasi-periodic schrödinger cocycles",
      "smooth topology",
      "zero lyapunov exponent",
      "smooth quasi-periodic cocycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150105380W"
    }
  }
}