{
  "id": "2208.00126",
  "version": "v1",
  "published": "2022-07-30T02:44:14.000Z",
  "updated": "2022-07-30T02:44:14.000Z",
  "title": "Rigidity of $\\mathbf{\\textit{U}}$-Gibbs measures near conservative Anosov diffeomorphisms on $\\mathbb{T}^3$",
  "authors": [
    "Sébastien Alvarez",
    "Martin Leguil",
    "Davi Obata",
    "Bruno Santiago"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that within a $C^1$-neighbourhood $\\mathcal{U}$ of the set of volume preserving Anosov diffeomorphisms on the three-torus $\\mathbb{T}^3$ which are strongly partially hyperbolic with expanding center, any $f\\in\\mathcal{U}\\cap\\operatorname{Diff}^2(\\mathbb{T}^3)$ satisfies the dichotomy: either the strong stable and unstable bundles $E^s$ and $E^u$ of $f$ are jointly integrable, or any fully supported $u$-Gibbs measure of $f$ is SRB.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-30T02:44:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conservative anosov diffeomorphisms",
      "gibbs measure",
      "volume preserving anosov diffeomorphisms",
      "three-torus",
      "strongly partially hyperbolic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}