{
  "id": "1407.6433",
  "version": "v1",
  "published": "2014-07-24T02:54:34.000Z",
  "updated": "2014-07-24T02:54:34.000Z",
  "title": "Bounds on the Lyapunov exponent via crude estimates on the density of states",
  "authors": [
    "Mira Shamis",
    "Thomas Spencer"
  ],
  "comment": "21pp",
  "categories": [
    "math-ph",
    "math.DS",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We study the Chirikov (standard) map at large coupling $\\lambda \\gg 1$, and prove that the Lyapounov exponent of the associated Schroedinger operator is of order $\\log \\lambda$ except for a set of energies of measure $\\exp(-c \\lambda^\\beta)$ for some $1 < \\beta < 2$. We also prove a similar (sharp) lower bound on the Lyapunov exponent (outside a small exceptional set of energies) for a large family of ergodic Schroedinger operators, the prime example being the $d$-dimensional skew shift.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-24T02:54:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lyapunov exponent",
      "crude estimates",
      "small exceptional set",
      "ergodic schroedinger operators",
      "dimensional skew shift"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-015-2324-x",
      "journal": "Communications in Mathematical Physics",
      "year": 2015,
      "month": "Sep",
      "pages": 705,
      "volume": 338,
      "number": 2
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015CMaPh.338..705S"
    }
  }
}