{
  "id": "0810.4661",
  "version": "v5",
  "published": "2008-10-27T02:31:31.000Z",
  "updated": "2012-02-23T09:06:23.000Z",
  "title": "Equidistribution of sparse sequences on nilmanifolds",
  "authors": [
    "Nikos Frantzikinakis"
  ],
  "comment": "32 pages. References updated, a few small changes made. Appeared in Journal d'Analyse Mathematique",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study equidistribution properties of nil-orbits $(b^nx)_{n\\in\\N}$ when the parameter $n$ is restricted to the range of some sparse sequence that is not necessarily polynomial. For example, we show that if $X=G/\\Gamma$ is a nilmanifold, $b\\in G$ is an ergodic nilrotation, and $c\\in \\R\\setminus \\Z$ is positive, then the sequence $(b^{[n^c]}x)_{n\\in\\N}$ is equidistributed in $X$ for every $x\\in X$. This is also the case when $n^c$ is replaced with $a(n)$, where $a(t)$ is a function that belongs to some Hardy field, has polynomial growth, and stays logarithmically away from polynomials, and when it is replaced with a random sequence of integers with sub-exponential growth. Similar results have been established by Boshernitzan when $X$ is the circle.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-02-23T09:06:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22F30",
      "37A17"
    ],
    "keywords": [
      "sparse sequence",
      "nilmanifold",
      "study equidistribution properties",
      "similar results",
      "hardy field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.4661F"
    }
  }
}