Chaotic behavior of group actions
Chaotic behavior of group actions
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DOI：
10.1090/conm/669/13434
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发表时间：
2015-03
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影响因子：
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通讯作者：
Zhaolong Wang;Guohua Zhang
中科院分区：
文献类型：
--
作者：
Zhaolong Wang;Guohua Zhang
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.
