{
  "id": "2206.13794",
  "version": "v1",
  "published": "2022-06-28T07:19:21.000Z",
  "updated": "2022-06-28T07:19:21.000Z",
  "title": "Thomae's function and the space of ergodic measures",
  "authors": [
    "Anton Gorodetski",
    "Alexandro Luna"
  ],
  "comment": "6 pages, 2 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the space of ergodic measures of the map $$f:\\mathbb{T}^2\\to \\mathbb{T}^2, \\ f(x, y)=(x, \\ x+y)(\\text{mod}\\, 1),$$ and show that its structure is similar to the graph of Thomae's function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-28T07:19:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E99"
    ],
    "keywords": [
      "ergodic measures",
      "thomaes function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}