{
  "id": "2406.10919",
  "version": "v1",
  "published": "2024-06-16T12:49:47.000Z",
  "updated": "2024-06-16T12:49:47.000Z",
  "title": "A new family of expansions of real numbers",
  "authors": [
    "Jörg Neunhäuserer"
  ],
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "For $\\alpha>1$ we represent a real number in $(0,1]$ in the form \\[ \\sum_{i=1}^{\\infty}(\\alpha-1)^{i-1}\\alpha^{-(d_{1}+\\dots+d_{i})}\\] with $d_{i}\\in\\mathbb{N}$. We discuss ergodic theoretical and dimension theoretical aspects of this expansion. Furthermore we study their base-change-transformation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-16T12:49:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K55",
      "37A44",
      "28A80",
      "26A30"
    ],
    "keywords": [
      "real number",
      "dimension theoretical aspects",
      "base-change-transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}