{
  "id": "1510.03202",
  "version": "v1",
  "published": "2015-10-12T09:48:31.000Z",
  "updated": "2015-10-12T09:48:31.000Z",
  "title": "Renormalizations of circle diffeomorphisms with a break-type singularity",
  "authors": [
    "Habibulla Akhadkulov",
    "Mohd Salmi Md Noorani",
    "Sokhobiddin Akhatkulov"
  ],
  "comment": "30 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be an orientation-preserving circle diffeomorphism with irrational rotation number and with a break point $\\xi_{0},$ that is, its derivative $f'$ has a discontinuity of the first kind at this point. Suppose that $f'$ satisfies a certain Zygmund condition dependent on a parameter $\\gamma>0.$ We prove that the renormalizations of $f$ are approximated by M\\\"{o}bius transformations in $C^{1}$-norm if $\\gamma\\in (0,1]$ and they are approximated in $C^{2}$-norm if $\\gamma\\in (1,+\\infty).$ Also it is shown, that the coefficients of M\\\"{o}bius transformations get asymptotically linearly dependent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-12T09:48:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C15",
      "37C40",
      "37E10",
      "37F25"
    ],
    "keywords": [
      "break-type singularity",
      "renormalizations",
      "irrational rotation number",
      "zygmund condition dependent",
      "orientation-preserving circle diffeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}