{
  "id": "1010.1223",
  "version": "v1",
  "published": "2010-10-06T18:35:27.000Z",
  "updated": "2010-10-06T18:35:27.000Z",
  "title": "Even order periodic operators on the real line",
  "authors": [
    "Andrey Badanin",
    "Evgeny Korotyaev"
  ],
  "comment": "35 pages, 4 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider $2p\\ge 4$ order differential operator on the real line with a periodic coefficients. The spectrum of this operator is absolutely continuous and is a union of spectral bands separated by gaps. We define the Lyapunov function, which is analytic on a p-sheeted Riemann surface. The Lyapunov function has real or complex branch points. We prove the following results: (1) The spectrum at high energy has multiplicity two. (2) Endpoints of all gaps are periodic (or anti-periodic) eigenvalues or real branch points. (3) The spectrum of operator has an infinite number of open gaps and there exists only a finite number of non-real branch points for some specific coefficients (the generic case). (4) The asymptotics of the periodic, anti-periodic spectrum and branch points are determined at high energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-06T18:35:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47E05",
      "34L20"
    ],
    "keywords": [
      "order periodic operators",
      "real line",
      "high energy",
      "lyapunov function",
      "complex branch points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.1223B"
    }
  }
}