{
  "id": "math/0602176",
  "version": "v1",
  "published": "2006-02-08T22:12:26.000Z",
  "updated": "2006-02-08T22:12:26.000Z",
  "title": "Measure rigidity beyond uniform hyperbolicity: Invariant Measures for Cartan actions on Tori",
  "authors": [
    "Boris Kalinin",
    "Anatole Katok"
  ],
  "comment": "28 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that every smooth action of Z^k, k>1, on the (k+1)-dimensional torus homotopic to an action by hyperbolic linear maps preserves an absolutely continuous measure. This is a first known result concerning abelian groups of diffeomorphisms where existence of an invariant geometric structure is obtained from homotopy data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-08T22:12:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C40",
      "37D25",
      "37C85"
    ],
    "keywords": [
      "uniform hyperbolicity",
      "invariant measures",
      "cartan actions",
      "measure rigidity",
      "hyperbolic linear maps preserves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2176K"
    }
  }
}