{
  "id": "1610.03213",
  "version": "v1",
  "published": "2016-10-11T07:00:31.000Z",
  "updated": "2016-10-11T07:00:31.000Z",
  "title": "On some generalizations of skew-shifts on $\\mathbb{T}^2$",
  "authors": [
    "Kristian Bjerklöv"
  ],
  "comment": "45 pages, 11 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we investigate maps of the two-torus $\\mathbb{T}^2$ of the form $T(x,y)=(x+\\omega,g(x)+f(y))$ for Diophantine $\\omega\\in\\mathbb{T}$ and for a class of maps $f,g:\\mathbb{T}\\to\\mathbb{T}$, where each $g$ is strictly monotone and of degree 2, and each $f$ is an orientation preserving circle homeomorphism. For our class of $f$ and $g$ we show that $T$ is minimal and has exactly two invariant and ergodic Borel probability measures. Moreover, these measures are supported on two $T$-invariant graphs. One of the graphs is a Strange Nonchaotic Attractor whose basin of attraction consists of (Lebesgue) almost all points in $\\mathbb{T}^2$. Only a low regularity assumption (Lipschitz) is needed on the maps $f$ and $g$, and the results are robust with respect to Lipschitz-small perturbations of $f$ and $g$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-11T07:00:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C40",
      "37C70",
      "37E30"
    ],
    "keywords": [
      "generalizations",
      "skew-shifts",
      "ergodic borel probability measures",
      "low regularity assumption",
      "strange nonchaotic attractor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}