{
  "id": "1807.09159",
  "version": "v1",
  "published": "2018-07-23T17:46:23.000Z",
  "updated": "2018-07-23T17:46:23.000Z",
  "title": "On the convergence of renormalizations of piecewise smooth homeomorphisms on the circle",
  "authors": [
    "Abdumajid Begmatov",
    "Kleyber Cunha"
  ],
  "comment": "13 pages. arXiv admin note: substantial text overlap with arXiv:1706.03654",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study renormalizations of piecewise smooth homeomorphisms on the circle, by considering such maps as generalized interval exchange maps of genus one. Suppose that $Df$ is absolutely continuous on each interval of continuity and $D\\ln{Df}\\in \\mathbb{L}_{p}$ for some $p>1$. We prove, that under certain combinatorial assumptions on $f_{1}$ and $f_{2}$, corresponding renormalizations approach to each other in $C^{1+L_{1}}$-norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-23T17:46:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E10",
      "37E05",
      "37E20",
      "37C05",
      "37B10"
    ],
    "keywords": [
      "piecewise smooth homeomorphisms",
      "convergence",
      "generalized interval exchange maps",
      "corresponding renormalizations approach",
      "study renormalizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}