{
  "id": "math/0411553",
  "version": "v1",
  "published": "2004-11-24T16:31:17.000Z",
  "updated": "2004-11-24T16:31:17.000Z",
  "title": "Semigroup actions on tori and stationary measures on projective spaces",
  "authors": [
    "Yves Guivarc'H",
    "Roman Urban"
  ],
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "Let $\\Gamma$ be a sub-semigroup of $G=GL(d,\\mathbb R),$ $d>1.$ We assume that the action of $\\Gamma$ on $\\R^d$ is strongly irreducible and that $\\Gamma$ contains a proximal and expanding element. We describe contraction properties of the dynamics of $\\Gamma$ on $\\R^d$ at infinity. This amounts to the consideration of the action of $\\Gamma$ on some compact homogeneous spaces of $G,$ which are extensions of the projective space $\\pr^{d-1}.$ In the case where $\\Gamma$ is a sub-semigroup of $GL(d,\\R)\\cap M(d,\\Z)$ and $\\Gamma$ has the above properties, we deduce that the $\\Gamma$-orbits on $\\T^d=\\R^d\\slash\\Z^d$ are finite or dense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-24T16:31:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H20",
      "22E40",
      "60J05",
      "60B15"
    ],
    "keywords": [
      "projective space",
      "stationary measures",
      "semigroup actions",
      "compact homogeneous spaces",
      "sub-semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11553G"
    }
  }
}