{
  "id": "2006.02028",
  "version": "v1",
  "published": "2020-06-03T03:41:23.000Z",
  "updated": "2020-06-03T03:41:23.000Z",
  "title": "Uniform distribution in nilmanifolds along functions from a Hardy field",
  "authors": [
    "Florian K. Richter"
  ],
  "comment": "45 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study equidistribution properties of translations on nilmanifolds along functions of polynomial growth from a Hardy field. More precisely, if $X=G/\\Gamma$ is a nilmanifold, $a_1,\\ldots,a_k\\in G$ are commuting nilrotations, and $f_1,\\ldots,f_k$ are functions of polynomial growth from a Hardy field then we show that $\\bullet$ the distribution of the sequence $a_1^{f_1(n)}\\cdot\\ldots\\cdot a_k^{f_k(n)}\\Gamma$ is governed by its projection onto the maximal factor torus, which extends Leibman's Equidistribution Criterion form polynomials to a much wider range of functions; and $\\bullet$ the orbit closure of $a_1^{f_1(n)}\\cdot\\ldots\\cdot a_k^{f_k(n)}\\Gamma$ is always a finite union of sub-nilmanifolds, which extends some of the previous work of Leibman and Frantzikinakis on this topic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-03T03:41:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hardy field",
      "uniform distribution",
      "nilmanifold",
      "leibmans equidistribution criterion form polynomials",
      "extends leibmans equidistribution criterion form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}