{
  "id": "math-ph/0105034",
  "version": "v1",
  "published": "2001-05-23T23:54:27.000Z",
  "updated": "2001-05-23T23:54:27.000Z",
  "title": "Uniform spectral properties of one-dimensional quasicrystals, IV. Quasi-Sturmian potentials",
  "authors": [
    "David Damanik",
    "Daniel Lenz"
  ],
  "comment": "20 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider discrete one-dimensional Schr\\\"odinger operators with quasi-Sturmian potentials. We present a new approach to the trace map dynamical system which is independent of the initial conditions and establish a characterization of the spectrum in terms of bounded trace map orbits. Using this, it is shown that the operators have purely singular continuous spectrum and their spectrum is a Cantor set of Lebesgue measure zero. We also exhibit a subclass having purely $\\alpha$-continuous spectrum. All these results hold uniformly on the hull generated by a given potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-05-23T23:54:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "47B80"
    ],
    "keywords": [
      "uniform spectral properties",
      "quasi-sturmian potentials",
      "one-dimensional quasicrystals",
      "trace map dynamical system",
      "lebesgue measure zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}