{
  "id": "1612.03454",
  "version": "v1",
  "published": "2016-12-11T19:09:28.000Z",
  "updated": "2016-12-11T19:09:28.000Z",
  "title": "Normal forms on contracting foliations: smoothness and homogeneous structure",
  "authors": [
    "Boris Kalinin",
    "Victoria Sadovskaya"
  ],
  "comment": "16 pages. arXiv admin note: text overlap with arXiv:1604.03963",
  "journal": "Geometriae Dedicata, Vol. 183 (2016), no. 1, 181-194",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we consider a diffeomorphism $f$ of a compact manifold $M$ which contracts an invariant foliation $W$ with smooth leaves. If the differential of $f$ on $TW$ has narrow band spectrum, there exist coordinates $H _x:W_x\\to T_xW$ in which $f|_W$ has polynomial form. We present a modified approach that allows us to construct maps $H_x$ that depend smoothly on $x$ along the leaves of $W$. Moreover, we show that on each leaf they give a coherent atlas with transition maps in a finite dimensional Lie group. Our results apply, in particular, to $C^1$-small perturbations of algebraic systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-11T19:09:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D30",
      "37D10",
      "34C20"
    ],
    "keywords": [
      "normal forms",
      "contracting foliations",
      "homogeneous structure",
      "smoothness",
      "finite dimensional lie group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}