{
  "id": "2204.11977",
  "version": "v1",
  "published": "2022-04-25T21:48:22.000Z",
  "updated": "2022-04-25T21:48:22.000Z",
  "title": "Surfaces of section for geodesic flows of closed surfaces",
  "authors": [
    "Gonzalo Contreras",
    "Gerhard Knieper",
    "Marco Mazzucchelli",
    "Benjamin H. Schulz"
  ],
  "comment": "32 pages, 11 figures",
  "categories": [
    "math.DG",
    "math.DS",
    "math.SG"
  ],
  "abstract": "We prove several results concerning the existence of surfaces of section for the geodesic flows of closed orientable Riemannian surfaces. The surfaces of section $\\Sigma$ that we construct are either Birkhoff sections, meaning that they intersect every sufficiently long orbit segment of the geodesic flow, or at least they have some hyperbolic components in $\\partial\\Sigma$ as limit sets of the orbits of the geodesic flow that do not return to $\\Sigma$. In order to prove these theorems, we provide a study of configurations of simple closed geodesics of closed orientable Riemannian surfaces, which may have independent interest. Our arguments are based on Grayson's curve shortening flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-25T21:48:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C22",
      "37D40",
      "53D25"
    ],
    "keywords": [
      "geodesic flow",
      "closed surfaces",
      "closed orientable riemannian surfaces",
      "sufficiently long orbit segment",
      "graysons curve shortening flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}