{
  "id": "2409.10004",
  "version": "v1",
  "published": "2024-09-16T05:28:28.000Z",
  "updated": "2024-09-16T05:28:28.000Z",
  "title": "Classification of horocycle orbit closures in $ \\mathbb{Z} $-covers",
  "authors": [
    "James Farre",
    "Or Landesberg",
    "Yair Minsky"
  ],
  "comment": "55 pages, 8 figures",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "We fully describe all horocycle orbit closures in $ \\mathbb{Z} $-covers of compact hyperbolic surfaces. Our results rely on a careful analysis of the efficiency of all distance minimizing geodesic rays in the cover. As a corollary we obtain in this setting that all non-maximal horocycle orbit closures, while fractal, have integer Hausdorff dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-16T05:28:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D40",
      "57K20",
      "37A17",
      "30F60",
      "22F30",
      "57K32",
      "37B20",
      "37B99"
    ],
    "keywords": [
      "classification",
      "non-maximal horocycle orbit closures",
      "compact hyperbolic surfaces",
      "integer hausdorff dimension",
      "distance minimizing geodesic rays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}