{
  "id": "1808.08849",
  "version": "v1",
  "published": "2018-08-27T13:59:38.000Z",
  "updated": "2018-08-27T13:59:38.000Z",
  "title": "Lipschitz equivalence of self-similar sets with exact overlaps",
  "authors": [
    "Kan Jiang",
    "Songjing Wang",
    "Lifeng Xi"
  ],
  "journal": "Ann.Acad.Sci.Fenn.Math., Volumen 43, 905-912, 2018",
  "categories": [
    "math.DS",
    "math.MG"
  ],
  "abstract": "In this paper, we study a class $\\mathcal{A}(\\lambda ,n,m)$ of self-similar sets with $m$ exact overlaps generated by $n$ similitudes of the same ratio $ \\lambda $. We obtain a necessary condition for a self-similar set in $\\mathcal{A}(\\lambda ,n,m)$ to be Lipschitz equivalent to a self-similar set satisfying the strong separation condition, i.e., there exists an integer $ k\\geq 2$ such that $x^{2k}-mx^{k}+n$ is reducible, in particular, $m$ belongs to $\\{a^{i}:a\\in \\mathbb{N}$ with $i\\geq 2\\}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-27T13:59:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact overlaps",
      "lipschitz equivalence",
      "strong separation condition",
      "lipschitz equivalent",
      "necessary condition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}