{
  "id": "1103.2591",
  "version": "v1",
  "published": "2011-03-14T06:51:56.000Z",
  "updated": "2011-03-14T06:51:56.000Z",
  "title": "Derivatives of rotation number of one parameter families of circle diffeomorphisms",
  "authors": [
    "Shigenori Matsumoto"
  ],
  "comment": "9 pages, 1 figure",
  "journal": "Kodai Mathematical Journal 35(2012), 115-125",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the rotation number $\\rho(t)$ of a diffeomorphism $f_t=R_t\\circ f$, where $R_t$ is the rotation by $t$ and $f$ is an orientation preserving $C^\\infty$ diffeomorphism of the circle $S^1$. We shall show that if $\\rho(t)$ is irrational $$\\limsup_{t'\\to t}(\\rho(t')-\\rho(t))/(t'-t)\\geq 1.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-14T06:51:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E10",
      "37E45"
    ],
    "keywords": [
      "rotation number",
      "parameter families",
      "circle diffeomorphisms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.2591M"
    }
  }
}