{
  "id": "2107.14058",
  "version": "v1",
  "published": "2021-07-29T14:49:59.000Z",
  "updated": "2021-07-29T14:49:59.000Z",
  "title": "The growth and distribution of large circles on translation surfaces",
  "authors": [
    "Paul Colognese",
    "Mark Pollicott"
  ],
  "comment": "26 pages, 6 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider circles on a translation surface $X$, consisting of points joined to a common center point by a geodesic of length $R$. We show that as $R \\to \\infty$ these circles distribute to a measure on $X$ which is equivalent to the area. In the last section we consider analogous results for closed geodesics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-29T14:49:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "translation surface",
      "large circles",
      "distribution",
      "common center point",
      "circles distribute"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}