{
  "id": "1505.02662",
  "version": "v1",
  "published": "2015-05-11T15:09:03.000Z",
  "updated": "2015-05-11T15:09:03.000Z",
  "title": "New Derived from Anosov Diffeomorphisms with pathological center foliation",
  "authors": [
    "F. Micena"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we focused our study on Derived From Anosov diffeomorphisms (DA diffeomorphisms ) of the torus $\\mathbb{T}^3,$ it is, an absolute partially hyperbolic diffeomorphism on $\\mathbb{T}^3$ homotopic to an Anosov linear automorphism of the $\\mathbb{T}^3.$ We can prove that if $f: \\mathbb{T}^3 \\rightarrow \\mathbb{T}^3 $ is a volume preserving DA diffeomorphism homotopic to linear Anosov $A,$ such that the center Lyapunov exponent satisfies $\\lambda^c_f(x) > \\lambda^c_A > 0,$ with $x $ belongs to a positive volume set, then the center foliation of $f$ is non absolutely continuous. We construct a new open class $U$ of non Anosov and volume preserving DA diffeomorphisms, satisfying the property $\\lambda^c_f(x) > \\lambda^c_A > 0$ for $m-$almost everywhere $x \\in \\mathbb{T}^3.$ Particularly for every $f \\in U,$ the center foliation of $f$ is non absolutely continuous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-11T15:09:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pathological center foliation",
      "anosov diffeomorphisms",
      "volume preserving da diffeomorphism homotopic",
      "center lyapunov exponent satisfies",
      "non absolutely continuous"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150502662M"
    }
  }
}