{
  "id": "1910.13536",
  "version": "v1",
  "published": "2019-10-29T21:14:34.000Z",
  "updated": "2019-10-29T21:14:34.000Z",
  "title": "Cantor Spectrum for CMV and Jacobi Matrices with Coefficients arising from Generalized Skew-Shifts",
  "authors": [
    "Hyunkyu Jun"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider continuous cocycles arising from CMV and Jacobi matrices. Assuming the Verblunsky and Jacobi coefficients arise from generalized skew-shifts, we prove that uniform hyperbolicity of the associated cocycles is $C^0$-dense. This implies that the associated CMV and Jacobi matrices have Cantor spectrum for a generic continuous sampling map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-29T21:14:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jacobi matrices",
      "cantor spectrum",
      "generalized skew-shifts",
      "coefficients arising",
      "jacobi coefficients arise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}