{
  "id": "1902.01300",
  "version": "v1",
  "published": "2019-02-04T16:45:02.000Z",
  "updated": "2019-02-04T16:45:02.000Z",
  "title": "Measure rigidity for horospherical subgroups of groups acting on regular trees",
  "authors": [
    "Corina Ciobotaru",
    "Vladimir Finkelshtein",
    "Cagri Sert"
  ],
  "comment": "33 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We investigate analogues of some of the classical results in homogeneous dynamics in non-linear setting. Let $G$ be a closed subgroup of the group of automorphisms of a $d$-regular tree and $\\Gamma<G$ a discrete subgroup. For a large class of groups $G$ we give a classification of probability measures on $G/\\Gamma$ invariant under horospherical subgroups. When $\\Gamma$ is a cocompact lattice, we prove unique ergodicity of the horospherical action. Moreover, for the family of Nagao quotients we prove Hedlund's theorem. Finally, we study equidistribution of large compact orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-04T16:45:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regular tree",
      "horospherical subgroups",
      "measure rigidity",
      "groups acting",
      "large compact orbits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}