{
  "id": "math/0608552",
  "version": "v1",
  "published": "2006-08-22T18:34:28.000Z",
  "updated": "2006-08-22T18:34:28.000Z",
  "title": "Parameter Families of Iterated Function Systems and Continuity",
  "authors": [
    "Maxwell Murphy"
  ],
  "comment": "7 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we investigate parameter families of iterated function systems and continuity. Specifically, if we have a set of iterated function systems that depend continuously on a parameter, which properties of the invariant sets will vary continuously? We show here that the invariant sets will vary continuously as a function of the parameter. Furthermore, we give some sufficient conditions under which the Hausdorff dimension will depend continuously on the parameter. Lastly, we give a counter-example where the dimension is not a continuous function of the parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-22T18:34:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80"
    ],
    "keywords": [
      "iterated function systems",
      "parameter families",
      "continuity",
      "invariant sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8552M"
    }
  }
}