{
  "id": "1305.7394",
  "version": "v3",
  "published": "2013-05-31T13:30:24.000Z",
  "updated": "2013-09-26T17:09:16.000Z",
  "title": "Shadowing for actions of some finitely generated groups",
  "authors": [
    "Alexey Osipov",
    "Sergey Tikhomirov"
  ],
  "comment": "18 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We introduce a notion of shadowing property for actions of finitely generated groups and study its basic properties. We formulate and prove a shadowing lemma for actions of nilpotent groups. We construct an example of a faithful linear action of a solvable Baumslag-Solitar group and show that the shadowing property depends on quantitative characteristics of hyperbolicity. Finally we show that any linear action of a non-abelian free group does not have the shadowing property.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-09-26T17:09:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C85",
      "37D20",
      "37C50"
    ],
    "keywords": [
      "finitely generated groups",
      "non-abelian free group",
      "shadowing property depends",
      "solvable baumslag-solitar group",
      "nilpotent groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.7394O"
    }
  }
}