{
  "id": "1910.10259",
  "version": "v1",
  "published": "2019-10-22T22:32:24.000Z",
  "updated": "2019-10-22T22:32:24.000Z",
  "title": "On the dimension spectra of infinite iterated function systems",
  "authors": [
    "Tushar Das",
    "David Simmons"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The dimension spectrum of an iterated function system (IFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. We construct a compact perfect subset of the nonnegative reals that cannot be realized as the dimension spectrum of a conformal IFS. We also provide an example of a similarity IFS whose dimension spectrum has zero Hausdorff dimension; in particular, such a dimension spectrum is not uniformly perfect. This resolves two questions posed by Chousionis, Leykekhman, and Urba\\'nski (Selecta, 2019), and provokes some new conjectures and questions regarding IFS dimension spectra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-22T22:32:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35",
      "28A80",
      "37B10"
    ],
    "keywords": [
      "dimension spectrum",
      "infinite iterated function systems",
      "questions regarding ifs dimension spectra",
      "subsystem limit sets",
      "zero hausdorff dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}