{
  "id": "math/0304469",
  "version": "v1",
  "published": "2003-04-28T21:53:59.000Z",
  "updated": "2003-04-28T21:53:59.000Z",
  "title": "On the cohomological equation for interval exchange maps",
  "authors": [
    "Stefano Marmi",
    "Pierre Moussa",
    "Jean-Christophe Yoccoz"
  ],
  "comment": "11 pages, french abstract and abridged version",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation $\\Psi -\\Psi\\circ T=\\Phi$ has a bounded solution $\\Psi$ provided that the datum $\\Phi$ belongs to a finite codimension subspace of the space of functions having on each interval a derivative of bounded variation. The class of interval exchange maps is characterized in terms of a diophantine condition of ``Roth type'' imposed to an acceleration of the Rauzy--Veech--Zorich continued fraction expansion associated to T. Contents 0. French abridged version 1. Interval exchange maps and the cohomological equation. Main Theorem 2. Rauzy--Veech--Zorich continued fraction algorithm and its acceleration 3. Special Birkhoff sums 4. The Diophantine condition 5. Sketch of the proof of the theorem",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-04-28T21:53:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cohomological equation",
      "continued fraction expansion",
      "diophantine condition",
      "explicit full measure class",
      "minimal interval exchange maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4469M"
    }
  }
}