{
  "id": "2501.10584",
  "version": "v1",
  "published": "2025-01-17T22:27:59.000Z",
  "updated": "2025-01-17T22:27:59.000Z",
  "title": "On the dimension theory of Okamoto's function",
  "authors": [
    "Balázs Bárány",
    "R. Dániel Prokaj"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we investigate the dimension theory of the one parameter family of Okamoto's function. We compute the Hausdorff, box-counting and Assouad dimensions of the graph for a typical choice of parameter. Furthermore, we study the dimension of the level sets. We give an upper bound on the dimension of every level set and we show that for a typical choice of parameters this value is attained for Lebesgue almost every level sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-17T22:27:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "37C45"
    ],
    "keywords": [
      "dimension theory",
      "okamotos function",
      "level set",
      "typical choice",
      "assouad dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}