{
  "id": "1512.03171",
  "version": "v1",
  "published": "2015-12-10T08:36:07.000Z",
  "updated": "2015-12-10T08:36:07.000Z",
  "title": "An open set of torus-maps conjugate to skew products",
  "authors": [
    "Suddhasattwa Das",
    "James Yorke"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We investigate conditions under which a map of the torus $\\Torus$ is conjugate to a skew-product dynamical system of the form $$(x_{n+1},y_{n+1})=(mx_n, g(x_n,y_n))\\mod 1,$$ where $m$ is an integer and $g:\\Torus\\to S^1$ is a $C^1$ map. Skew-product maps are relatively easy to analyze and include a variety of interesting dynamical systems. Notice that the dynamics in the X coordinate is $x_{n+1}=mx_n\\mod 1$. We present sufficient conditions for a torus map to be conjugate to a skew-product map. The set of maps which satisfy these conditions is open in the $C^1$ topology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-10T08:36:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37C15"
    ],
    "keywords": [
      "open set",
      "torus-maps conjugate",
      "skew products",
      "skew-product map",
      "skew-product dynamical system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}