{
  "id": "1802.08266",
  "version": "v1",
  "published": "2018-02-22T19:00:23.000Z",
  "updated": "2018-02-22T19:00:23.000Z",
  "title": "Lyapunov exponents and rigidity of Anosov automorphisms and skew products",
  "authors": [
    "Radu Saghin",
    "Jiagang Yang"
  ],
  "comment": "preliminary version",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we obtain local rigidity results for linear Anosov diffeomorphisms in terms of Lyapunov exponents. More specifically, we show that given an irreducible linear hyperbolic automorphism $L$ with simple real spectrum, any small perturbation preserving the volume and with the same Lyapunov exponents is smoothly conjugate to $L$. We also obtain rigidity results for skew products over Anosov diffeomorphisms. Given a volume preserving partially hyperbolic skew product diffeomorphism $f_0$ over an Anosov automorphism of the 2-torus, we show that for any volume preserving perturbation $f$ of $f_0$ with the same average stable and unstable Lyapunov exponents, the center foliation is smooth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-22T19:00:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lyapunov exponents",
      "anosov automorphism",
      "preserving partially hyperbolic skew",
      "anosov diffeomorphisms",
      "rigidity results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}