{
  "id": "1912.10265",
  "version": "v1",
  "published": "2019-12-21T13:28:22.000Z",
  "updated": "2019-12-21T13:28:22.000Z",
  "title": "Hotspot lemmas for non-compact spaces",
  "authors": [
    "Dylan Airey",
    "Bill Mance"
  ],
  "comment": "4 pages",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We extend the hotspot lemma, or Piatetski\\u{i}-Shapiro normality criterion, to dynamical systems on non-compact spaces. We build on the work of N. G. Moshchevitin and I. D. Shkredov, noting an issue in some of their proofs, and adding a necessary and sufficient condition to remove this issue.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-21T13:28:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "11A63",
      "11K16",
      "11K50"
    ],
    "keywords": [
      "non-compact spaces",
      "hotspot lemma",
      "normality criterion",
      "sufficient condition",
      "dynamical systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}