{
  "id": "2201.10156",
  "version": "v1",
  "published": "2022-01-25T08:00:02.000Z",
  "updated": "2022-01-25T08:00:02.000Z",
  "title": "Superdensity and bounded geodesics in moduli space",
  "authors": [
    "Josh Southerland"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "Following Beck-Chen, we say a flow $\\phi_t$ on a metric space $(X, d)$ is superdense if there is a $c > 0$ such that for every $x \\in X$, and every $T>0$, the trajectory $\\{\\phi_t x\\}_{0 \\le t \\le cT}$ is $1/T$-dense in $X$. We show that a linear flow on a translation surface is superdense if and only if the associated Teichm\\\"uller geodesic is bounded. This generalizes work of Beck-Chen on lattice surfaces, and is reminiscent of work of Masur on unique ergodicity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-25T08:00:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E35",
      "30F30",
      "30F60"
    ],
    "keywords": [
      "moduli space",
      "bounded geodesics",
      "superdensity",
      "metric space",
      "superdense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}