{
  "id": "1906.07250",
  "version": "v1",
  "published": "2019-06-17T20:26:27.000Z",
  "updated": "2019-06-17T20:26:27.000Z",
  "title": "On Cross Sections to the Geodesic and Horocycle Flows on Quotients of $\\operatorname{SL}(2, \\mathbb{R})$ by Hecke Triangle Groups $G_q$",
  "authors": [
    "Diaaeldin Taha"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we provide a model for cross sections to the geodesic and horocycle flows on $\\operatorname{SL}(2, \\mathbb{R})/G_q$ using an extension of a heuristic of P. Arnoux and A. Nogueira. Our starting point is a continued fraction algorithm related to the group $G_q$, and a cross section to the horocycle flow on $\\operatorname{SL}(2, \\mathbb{R})/G_q$ from a previous paper. As an application, we get the natural extension and invariant measure for a symmetric $G_q$-Farey interval map resulting from projectivizing the aforementioned continued fraction algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-17T20:26:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "horocycle flow",
      "hecke triangle groups",
      "cross section",
      "farey interval map",
      "aforementioned continued fraction algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}