{
  "id": "math-ph/0405061",
  "version": "v2",
  "published": "2004-05-25T19:28:17.000Z",
  "updated": "2014-12-30T01:19:26.000Z",
  "title": "Almost Everywhere Positivity of the Lyapunov Exponent for the Doubling Map",
  "authors": [
    "David Damanik",
    "Rowan Killip"
  ],
  "comment": "4 pages",
  "journal": "Commun. Math. Phys. 257 (2005), 287-290",
  "doi": "10.1007/s00220-004-1261-x",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We show that discrete one-dimensional Schr\\\"odinger operators on the half-line with ergodic potentials generated by the doubling map on the circle, $V_\\theta(n) = f(2^n \\theta)$, may be realized as the half-line restrictions of a non-deterministic family of whole-line operators. As a consequence, the Lyapunov exponent is almost everywhere positive and the absolutely continuous spectrum is almost surely empty.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-25T19:28:17.000Z",
      "journal": null
    },
    {
      "version": "v2",
      "updated": "2014-12-30T01:19:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lyapunov exponent",
      "doubling map",
      "positivity",
      "ergodic potentials",
      "whole-line operators"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}