{
  "id": "1105.5965",
  "version": "v3",
  "published": "2011-05-30T12:40:41.000Z",
  "updated": "2011-11-09T11:17:22.000Z",
  "title": "Stepped surfaces and Rauzy fractals induced from automorphisms on the free group of rank 2",
  "authors": [
    "Hiromi Ei"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For substitution satisfying Pisot, irreducible, unimodular condition, a tiling substitution plays a key role in construction of a stepped surface and Rauzy fractal. In this paper we will extend the method to hyperbolic automorphisms on the free group of rank 2 in some class, and obtain set equations of Rauzy fractals by virtue of a tiling substitution. We will also see that the domain exchange transformation on Rauzy fractal is just a two interval exchange transformation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-09T11:17:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free group",
      "rauzy fractals",
      "stepped surface",
      "domain exchange transformation",
      "tiling substitution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.5965E"
    }
  }
}