{
  "id": "1406.5314",
  "version": "v1",
  "published": "2014-06-20T08:43:42.000Z",
  "updated": "2014-06-20T08:43:42.000Z",
  "title": "Self-similar subsets of the Cantor set",
  "authors": [
    "De-Jun Feng",
    "Hui Rao",
    "Yang Wang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we study the following question raised by Mattila in 1998: what are the self-similar subsets of the middle-third Cantor set $\\C$? We give criteria for a complete classification of all such subsets. We show that for any self-similar subset $\\F$ of $\\C$ containing more than one point every linear generating IFS of $\\F$ must consist of similitudes with contraction ratios $\\pm 3^{-n}$, $n\\in \\N$. In particular, a simple criterion is formulated to characterize self-similar subsets of $\\C$ with equal contraction ratio in modulus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-20T08:43:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78",
      "28A80",
      "11K16"
    ],
    "keywords": [
      "middle-third cantor set",
      "equal contraction ratio",
      "simple criterion",
      "characterize self-similar subsets",
      "complete classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.5314F"
    }
  }
}