{
  "id": "math/0512192",
  "version": "v1",
  "published": "2005-12-09T11:27:03.000Z",
  "updated": "2005-12-09T11:27:03.000Z",
  "title": "On the cohomological equation for nilflows",
  "authors": [
    "Livio Flaminio",
    "Giovanni Forni"
  ],
  "comment": "27 pages",
  "journal": "Journal of Modern Dynamics (JMD), Pages: 37 - 60, Issue 1, January 2007",
  "doi": "10.3934/jmd.2007.1.37",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let X be a vector field on a compact connected manifold M. An important question in dynamical systems is to know when a function g:M -> R is a coboundary for the flow generated by X, i.e. when there exists a function f: M->R such that Xf=g. In this article we investigate this question for nilflows on nilmanifolds. We show that there exists countably many independent Schwartz distributions D_n such that any sufficiently smooth function g is a coboundary iff it belongs to the kernel of all the distributions D_n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-09T11:27:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28Dxx",
      "43A85",
      "22E27",
      "22E40",
      "58J42"
    ],
    "keywords": [
      "cohomological equation",
      "independent schwartz distributions",
      "vector field",
      "sufficiently smooth function",
      "compact connected manifold"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12192F"
    }
  }
}