{
  "id": "1705.05422",
  "version": "v1",
  "published": "2017-05-15T19:46:59.000Z",
  "updated": "2017-05-15T19:46:59.000Z",
  "title": "Pathological center foliation with dimension greater than one",
  "authors": [
    "J. S. Costa",
    "F. Micena"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we are considering partially hyperbolic diffeomorphims of the torus, with $dim(E^c) > 1.$ We prove, under some conditions, that if the all center Lyapunov exponents of the linearization $A,$ of a \\mbox{DA-diffeomorphism} $f,$ are positive and the center foliation of $f$ is absolutely continuous, then the sum of the center Lyapunov exponents of $f$ is bounded by the sum of the center Lyapunov exponents of $A.$ After, we construct a $C^1-$open class of volume preserving \\mbox{DA-diffeomorphisms}, far from Anosov diffeomorphisms, with non compact pathological two dimensional center foliation. Indeed, each $f$ in this open set satisfies the previously established hypothesis, but the sum of the center Lyapunov exponents of $f$ is greater than the corresponding sum with respect to its linearization. It allows to conclude that the center foliation of $f$ is non absolutely continuous. We still build an example of a DA-diffeomorphism, such that the disintegration of volume along the two dimensional, non compact center foliation is neither Lebesgue nor atomic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-15T19:46:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "center lyapunov exponents",
      "pathological center foliation",
      "dimension greater",
      "non compact center foliation",
      "open set satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}