{
  "id": "1905.03961",
  "version": "v1",
  "published": "2019-05-10T06:27:53.000Z",
  "updated": "2019-05-10T06:27:53.000Z",
  "title": "Generic point equivalence and Pisot numbers",
  "authors": [
    "Shigeki Akiyama",
    "Hajime Kaneko",
    "Dong Han Kim"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "Let $\\beta >1$ be an integer or generally a Pisot number. Put $T(x) = \\{ \\beta x \\}$ on $[0,1]$ and let $S: [0,1]\\to [0,1]$ be a piecewise linear transformation whose slopes have the form $\\pm \\beta^m$ with positive integers $m$. We give sufficient conditions that $T$ and $S$ have the same generic points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-10T06:27:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K16",
      "37E05"
    ],
    "keywords": [
      "generic point equivalence",
      "pisot number",
      "sufficient conditions",
      "piecewise linear transformation",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}