{
  "id": "0711.2307",
  "version": "v4",
  "published": "2007-11-14T21:45:22.000Z",
  "updated": "2015-04-15T17:23:43.000Z",
  "title": "Horocycle flows for laminations by hyperbolic Riemann surfaces and Hedlund's theorem",
  "authors": [
    "Matilde Martínez",
    "Shigenori Matsumoto",
    "Alberto Verjovsky"
  ],
  "comment": "Corrected version of previous paper \"Hedlund's theorem for compact minimal laminations\"",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the dynamics of the geodesic and horocycle flows of the unit tangent bundle $(\\hat M, T^1\\mathcal{F})$ of a compact minimal lamination $(M,\\mathcal F)$ by negatively curved surfaces. We give conditions under which the action of the affine group generated by the joint action of these flows is minimal, and examples where this action is not minimal. In the first case, we prove that if $\\mathcal F$ has a leaf which is not simply connected, the horocyle flow is topologically transitive.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-11-21T21:54:46.000Z",
      "abstract": "We study the dynamics of the geodesic and horocycle flows of the unit tangent bundle $(\\hat{M}, T^1\\mathcal{F})$ of a compact lamination $(M,\\mathcal{F})$ by negatively curved surfaces. We show the dichotomy: either the action of the affine group generated by the joint action of these flows is minimal, or the lamination is given by the orbits of a locally free action of the affine group on $M$. In the first case, we prove that if $\\mathcal{F}$ has a leaf which is not simply connected,the horocyle flow is topologically transitive.",
      "journal": null,
      "doi": null,
      "authors": [
        "Matilde Martínez",
        "Alberto Verjovsky"
      ]
    },
    {
      "version": "v4",
      "updated": "2015-04-15T17:23:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D40",
      "37A17",
      "58J65"
    ],
    "keywords": [
      "hyperbolic riemann surfaces",
      "horocycle flows",
      "hedlunds theorem",
      "affine group",
      "unit tangent bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2307M"
    }
  }
}