{
  "id": "1104.4502",
  "version": "v1",
  "published": "2011-04-22T20:10:38.000Z",
  "updated": "2011-04-22T20:10:38.000Z",
  "title": "Limit Theorems for Horocycle Flows",
  "authors": [
    "Alexander Bufetov",
    "Giovanni Forni"
  ],
  "comment": "52 pages",
  "categories": [
    "math.DS",
    "math.PR",
    "math.RT"
  ],
  "abstract": "The main results of this paper are limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the paper is a special family of horocycle-invariant finitely-additive Hoelder measures on rectifiable arcs. An asymptotic formula for ergodic integrals for horocycle flows is obtained in terms of the finitely-additive measures, and limit theorems follow as a corollary of the asymptotic formula. The objects and results of this paper are similar to those in [15], [16], [4] and [5] for translation flows on flat surfaces. The arguments are based on the classification of invariant distributions for horocycle flows established in [12].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-22T20:10:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D40",
      "37A17",
      "37A50",
      "22E46",
      "60B10"
    ],
    "keywords": [
      "horocycle flows",
      "limit theorems",
      "asymptotic formula",
      "horocycle-invariant finitely-additive hoelder measures",
      "compact surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4502B"
    }
  }
}