{
  "id": "1505.05746",
  "version": "v1",
  "published": "2015-05-21T14:10:27.000Z",
  "updated": "2015-05-21T14:10:27.000Z",
  "title": "Dimension approximation of attractors of graph directed IFSs by self-similar sets",
  "authors": [
    "Ábel Farkas"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1307.2841",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that for the attractor $(K_{1},\\dots,K_{q})$ of a graph directed iterated function system, for each $1\\leq j\\leq q$ and $\\varepsilon>0$ there exits a self-similar set $K\\subseteq K_{j}$ that satisfies the strong separation condition and $\\dim_{H}K_{j}-\\varepsilon<\\dim_{H}K$. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of $K$. Using this property we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-21T14:10:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "28A78",
      "37C45"
    ],
    "keywords": [
      "graph directed ifss",
      "self-similar set",
      "dimension approximation",
      "assume convenient conditions",
      "strong separation condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150505746F"
    }
  }
}