{
  "id": "1403.2937",
  "version": "v2",
  "published": "2014-03-12T14:05:22.000Z",
  "updated": "2015-12-17T10:15:20.000Z",
  "title": "SRB measures for partially hyperbolic systems whose central direction is weakly expanding",
  "authors": [
    "Jose F. Alves",
    "C. L. Dias",
    "S. Luzzatto",
    "V. Pinheiro"
  ],
  "comment": "Revised version",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider partially hyperbolic \\( C^{1+} \\) diffeomorphisms of compact Riemannian manifolds of arbitrary dimension which admit a partially hyperbolic tangent bundle decomposition \\( E^s\\oplus E^{cu} \\). Assuming the existence of a set of positive Lebesgue measure on which \\( f \\) satisfies a weak nonuniform expansivity assumption in the centre~unstable direction, we prove that there exists at most a finite number of transitive attractors each of which supports an SRB measure. As part of our argument, we prove that each attractor admits a Gibbs-Markov-Young geometric structure with integrable return times. We also characterize in this setting SRB measures which are liftable to Gibbs-Markov-Young structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-12T14:05:22.000Z",
      "comment": "26 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-12-17T10:15:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "srb measure",
      "partially hyperbolic systems",
      "central direction",
      "weakly expanding",
      "weak nonuniform expansivity assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.2937A"
    }
  }
}