{
  "id": "1503.02176",
  "version": "v1",
  "published": "2015-03-07T14:14:25.000Z",
  "updated": "2015-03-07T14:14:25.000Z",
  "title": "Chaotic behavior of group actions",
  "authors": [
    "Zhaolong Wang",
    "Guohua Zhang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we study chaotic behavior of actions of a countable discrete group acting on a compact metric space by self-homeomorphisms. For actions of a countable discrete group G, we introduce local weak mixing and Li-Yorke chaos; and prove that local weak mixing implies Li-Yorke chaos if G is infinite, and positive topological entropy implies local weak mixing if G is an infinite countable discrete amenable group. Moreover, when considering a shift of finite type for actions of an infinite countable amenable group G, if the action has positive topological entropy then its homoclinic equivalence relation is non-trivial, and the converse holds true if additionally G is residually finite and the action contains a dense set of periodic points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-07T14:14:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chaotic behavior",
      "entropy implies local weak",
      "group actions",
      "topological entropy implies local",
      "weak mixing implies li-yorke"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}