{
  "id": "1805.12288",
  "version": "v1",
  "published": "2018-05-31T02:07:19.000Z",
  "updated": "2018-05-31T02:07:19.000Z",
  "title": "A Note on Rigidity of Anosov diffeomorphisms of the Three Torus",
  "authors": [
    "F. Micena",
    "A. Tahzibi"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider Anosov diffeomorphisms on $\\mathbb{T}^3$ such that the tangent bundle splits into three subbundles $E^s_f \\oplus E^{wu}_f \\oplus E^{su}_f.$ We show that if $f$ is $C^r, r \\geq 2,$ volume preserving, then $f$ is $C^1$ conjugated with its linear part $A$ if and only if the center foliation $\\mathcal{F}^{wu}_f$ is absolutely continuous and the equality $\\lambda^{wu}_f(x) = \\lambda^{wu}_A,$ between center Lyapunov exponents of $f$ and $A,$ holds for $m$ a.e. $x \\in \\mathbb{T}^3.$ We also conclude rigidity of derived from Anosov diffeomorphism, assuming an strong absolute continuity property (Uniform bounded density property) of strong stable and strong unstable foliations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-31T02:07:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anosov diffeomorphism",
      "strong absolute continuity property",
      "center lyapunov exponents",
      "tangent bundle splits",
      "uniform bounded density property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}