{
  "id": "2001.06073",
  "version": "v1",
  "published": "2020-01-16T21:26:00.000Z",
  "updated": "2020-01-16T21:26:00.000Z",
  "title": "Geodesic flows and the mother of all continued fractions",
  "authors": [
    "Claire Merriman"
  ],
  "comment": "12 pages, 4 figures",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We extend the Series' connection between the modular surface $\\mathcal{M}=\\operatorname{PSL}(2,\\mathbb{Z})\\backslash\\mathbb{H}$, cutting sequences, and regular continued fractions to the slow converging Lehner and Farey continued fractions with digits $(1,+1)$ and $(2,-1)$. We also introduce an alternative insertion and singularization algorithm for Farey expansions and other non-semiregular continued fractions, and an alternative dual expansion to the Farey expansions so that $\\frac{dxdy}{(1+xy)^2}$ is invariant under the natural extension map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-16T21:26:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geodesic flows",
      "farey expansions",
      "natural extension map",
      "modular surface",
      "alternative dual expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}