{
  "id": "2212.10944",
  "version": "v1",
  "published": "2022-12-21T11:35:28.000Z",
  "updated": "2022-12-21T11:35:28.000Z",
  "title": "Rotation number of 2-interval piecewise affine maps",
  "authors": [
    "José Pedro Gaivao",
    "Michel Laurent",
    "Arnaldo Nogueira"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $f_{\\p}$ are parametrized by a quintuple $\\p$ of real numbers satisfying inequations. Viewing $f_{\\p}$ as a circle map, we show that it has a rotation number $\\rho(f_{\\p})$ and we compute $\\rho(f_{\\p})$ as a function of $\\p$ in terms of Hecke-Mahler series. As a corollary, we prove that $\\rho(f_{\\p})$ is a rational number when the components of $\\p$ are algebraic numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-21T11:35:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "piecewise affine maps",
      "rotation number",
      "real numbers satisfying inequations",
      "study maps",
      "hecke-mahler series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}