{
  "id": "1506.08033",
  "version": "v1",
  "published": "2015-06-26T11:37:43.000Z",
  "updated": "2015-06-26T11:37:43.000Z",
  "title": "Attractors of Iterated Function Systems with uncountably many maps",
  "authors": [
    "Giorgio Mantica",
    "Roberto Peirone"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "nlin.CD"
  ],
  "abstract": "We study the topological properties of attractors of Iterated Function Systems (I.F.S.) on the real line, consisting of affine maps of homogeneous contraction ratio. These maps define what we call a second generation I.F.S.: they are uncountably many and the set of their fixed points is a Cantor set. We prove that when this latter either is the attractor of a finite, non-singular, hyperbolic, I.F.S. (of first generation), or it possesses a particular dissection property, the attractor of the second generation I.F.S. consists of finitely many closed intervals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-26T11:37:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "37C20",
      "37E05"
    ],
    "keywords": [
      "iterated function systems",
      "second generation",
      "uncountably",
      "real line",
      "cantor set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}