{
  "id": "1009.2994",
  "version": "v2",
  "published": "2010-09-15T18:47:11.000Z",
  "updated": "2012-01-17T19:35:15.000Z",
  "title": "Local rigidity for Anosov automorphisms",
  "authors": [
    "Andrey Gogolev",
    "Boris Kalinin",
    "Victoria Sadovskaya"
  ],
  "comment": "18 pages, 2 figures, with an Appendix by Rafael de la Llave. Some minor fixes in the second version",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider an irreducible Anosov automorphism L of a torus T^d such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C^1 conjugate to any C^1-small perturbation f with the same periodic data. We also prove that toral automorphisms satisfying these assumptions are generic in SL(d,Z). Examples constructed in the Appendix by Rafael de la Llave show importance of the assumption on the eigenvalues.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-17T19:35:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C15",
      "37D20"
    ],
    "keywords": [
      "local rigidity",
      "assumption",
      "periodic data",
      "eigenvalues",
      "irreducible anosov automorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.2994G"
    }
  }
}