{
  "id": "1611.01196",
  "version": "v1",
  "published": "2016-11-03T21:14:37.000Z",
  "updated": "2016-11-03T21:14:37.000Z",
  "title": "Attractors of sequences of iterated function systems",
  "authors": [
    "Ryan Broderick"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "If $F$ and $G$ are iterated function systems, then any infinite word $W$ in the symbols $F$ and $G$ induces a limit set. It is natural to ask whether this Cantor set can also be realized as the limit set of a single $C^{1 + \\alpha}$ iterated function system $H$. We prove that under certain assumptions on $F$ and $G$, the answer is no. This problem is motivated by the spectral theory of one-dimensional quasicrystals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-03T21:14:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "iterated function system",
      "attractors",
      "limit set",
      "cantor set",
      "infinite word"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}