{
  "id": "math/0406360",
  "version": "v1",
  "published": "2004-06-18T04:35:11.000Z",
  "updated": "2004-06-18T04:35:11.000Z",
  "title": "Convergence of multiple ergodic averages for some commuting transformations",
  "authors": [
    "Nikos Frantzikinakis",
    "Bryna Kra"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove the $L^{2}$ convergence for the linear multiple ergodic averages of commuting transformations $T_{1}, ..., T_{l}$, assuming that each map $T_i$ and each pair $T_iT_j^{-1}$ is ergodic for $i\\neq j$. The limiting behavior of such averages is controlled by a particular factor, which is an inverse limit of nilsystems. As a corollary we show that the limiting behavior of linear multiple ergodic averages is the same for commuting transformations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-18T04:35:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30"
    ],
    "keywords": [
      "commuting transformations",
      "linear multiple ergodic averages",
      "convergence",
      "limiting behavior",
      "inverse limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6360F"
    }
  }
}