{
  "id": "1804.02879",
  "version": "v1",
  "published": "2018-04-09T09:25:45.000Z",
  "updated": "2018-04-09T09:25:45.000Z",
  "title": "On the continuity of the Hausdorff dimension of the univoque set",
  "authors": [
    "Pieter Allaart",
    "Derong Kong"
  ],
  "comment": "18 pages",
  "doi": "10.1016/j.aim.2019.106729",
  "categories": [
    "math.DS"
  ],
  "abstract": "In a recent paper [Adv. Math. 305:165--196, 2017], Komornik et al.~proved a long-conjectured formula for the Hausdorff dimension of the set $\\mathcal{U}_q$ of numbers having a unique expansion in the (non-integer) base $q$, and showed that this Hausdorff dimension is continuous in $q$. Unfortunately, their proof contained a gap which appears difficult to fix. This article gives a completely different proof of these results, using a more direct combinatorial approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-09T09:25:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "37B10",
      "28A78"
    ],
    "keywords": [
      "hausdorff dimension",
      "univoque set",
      "continuity",
      "direct combinatorial approach",
      "unique expansion"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}