{
  "id": "math/0205044",
  "version": "v1",
  "published": "2002-05-06T09:42:29.000Z",
  "updated": "2002-05-06T09:42:29.000Z",
  "title": "Polynomial growth of the derivative for diffeomorphisms on tori",
  "authors": [
    "Krzysztof Fraczek"
  ],
  "comment": "41 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider area--preserving diffeomorphisms on tori with zero entropy. We classify ergodic area--preserving diffeomorphisms of the 3--torus for which the sequence $\\{Df^n\\}_{n\\in{\\Bbb N}}$ has polynomial growth. Roughly speaking, the main theorem says that every ergodic area--preserving $C^2$--diffeomorphism with polynomial uniform growth of the derivative is $C^2$--conjugate to a 2--steps skew product of the form \\[\\tor^3\\ni(x_1,x_2,x_3)\\mapsto (x_1+\\alpha,\\ep x_2+\\beta(x_1),x_3+\\gamma(x_1,x_2))\\in\\tor^3,\\] where $\\ep=\\pm 1$. We also indicate why there is no 4--dimensional analogue of the above result. Random diffeomorphisms on the 2--torus are studied as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-05-06T09:42:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37C05",
      "37C40"
    ],
    "keywords": [
      "polynomial growth",
      "polynomial uniform growth",
      "derivative",
      "main theorem says",
      "random diffeomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......5044F"
    }
  }
}