{
  "id": "1002.2942",
  "version": "v1",
  "published": "2010-02-15T20:30:53.000Z",
  "updated": "2010-02-15T20:30:53.000Z",
  "title": "Rigidity of real-analytic actions of $SL(n,\\Z)$ on $\\T^n$: A case of realization of Zimmer program",
  "authors": [
    "Anatole Katok",
    "Federico Rodriguez Hertz"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that any real-analytic action of $SL(n,\\Z), n\\ge 3$ with standard homotopy data that preserves an ergodic measure $\\mu$ whose support is not contained in a ball, is analytically conjugate on an open invariant set to the standard linear action on the complement to a finite union of periodic orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-15T20:30:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real-analytic action",
      "zimmer program",
      "realization",
      "standard homotopy data",
      "open invariant set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.2942K"
    }
  }
}