{
  "id": "1210.0816",
  "version": "v2",
  "published": "2012-10-02T16:00:31.000Z",
  "updated": "2014-09-22T21:49:19.000Z",
  "title": "Gap distributions and homogeneous dynamics",
  "authors": [
    "Jayadev S. Athreya"
  ],
  "comment": "to appear in Proceedings of ICM Satellite Conference on Geometry, Topology, and Dynamics in Negative Curvarture",
  "categories": [
    "math.DS",
    "math.GT",
    "math.NT"
  ],
  "abstract": "We survey the use of dynamics of $SL(2, \\R)$-actions to understand gap distributions for various sequences of subsets of $[0, 1)$, particularly those arising from special trajectories of various two-dimensional dynamical systems. We state and prove an abstract theorem that gives a unified explanation for some of the examples we present.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-02T16:00:31.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-22T21:49:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D40",
      "30F30",
      "11B57"
    ],
    "keywords": [
      "homogeneous dynamics",
      "understand gap distributions",
      "abstract theorem",
      "special trajectories",
      "two-dimensional dynamical systems"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.0816A"
    }
  }
}