{
  "id": "1306.0445",
  "version": "v1",
  "published": "2013-06-03T14:57:34.000Z",
  "updated": "2013-06-03T14:57:34.000Z",
  "title": "Analytic expanding circle maps with explicit spectra",
  "authors": [
    "Julia Slipantschuk",
    "Oscar F. Bandtlow",
    "Wolfram Just"
  ],
  "comment": "15 pages, 3 figures",
  "categories": [
    "math.DS",
    "math.SP",
    "nlin.CD"
  ],
  "abstract": "We show that for any $\\lambda \\in \\mathbb{C}$ with $|\\lambda|<1$ there exists an analytic expanding circle map such that the eigenvalues of the associated transfer operator (acting on holomorphic functions) are precisely the nonnegative powers of $\\lambda$ and $\\bar{\\lambda}$. As a consequence we obtain a counterexample to a variant of a conjecture of Mayer on the reality of spectra of transfer operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-03T14:57:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05",
      "37E10",
      "37A25",
      "47A35"
    ],
    "keywords": [
      "analytic expanding circle map",
      "explicit spectra",
      "associated transfer operator",
      "holomorphic functions",
      "consequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}