{
  "id": "1907.08655",
  "version": "v1",
  "published": "2019-07-19T19:24:43.000Z",
  "updated": "2019-07-19T19:24:43.000Z",
  "title": "Dynamics of 2-interval piecewise affine maps and Hecke-Mahler series",
  "authors": [
    "Michel Laurent",
    "Arnaldo Nogueira"
  ],
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "Let $f : [0,1)\\rightarrow [0,1)$ be a $2$-interval piecewise affine increasing map which is injective but not surjective. Such a map $f$ has a rotation number and can be parametrized by three real numbers. We make fully explicit the dynamics of $f$ thanks to two specific functions $\\delta$ and $\\phi$ depending on these parameters whose definitions involve Hecke-Mahler series. As an application, we show that the rotation number of $f$ is rational, when the three parameters are algebraic numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-19T19:24:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "piecewise affine maps",
      "hecke-mahler series",
      "rotation number",
      "interval piecewise affine increasing map",
      "real numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}