{
  "id": "1405.7008",
  "version": "v1",
  "published": "2014-05-27T18:56:12.000Z",
  "updated": "2014-05-27T18:56:12.000Z",
  "title": "Exponential Mixing for Skew Products with Discontinuities",
  "authors": [
    "Oliver Butterley",
    "Peyman Eslami"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the skew product $F: (x,u) \\mapsto (f(x), u + \\tau(x))$, where the base map $f : \\mathbb{T}^{1} \\to \\mathbb{T}^{1}$ is piecewise $\\mathcal{C}^{2}$, covering and uniformly expanding, and the fibre map $\\tau : \\mathbb{T}^{1} \\to \\mathbb{R}$ is piecewise $\\mathcal{C}^{2}$. We show the dichotomy that either this system mixes exponentially or $\\tau$ is cohomologous (via a Lipschitz function) to a piecewise constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-27T18:56:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A25",
      "37C30",
      "37D50"
    ],
    "keywords": [
      "skew product",
      "exponential mixing",
      "discontinuities",
      "lipschitz function",
      "fibre map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.7008B"
    }
  }
}