Markovian properties of continuous group actions: Algebraic actions, entropy and the homoclinic group
Markovian properties of continuous group actions: Algebraic actions, entropy and the homoclinic group
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DOI：
10.1016/j.aim.2022.108196
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发表时间：
2019-11
影响因子：
1.7
通讯作者：
S. Barbieri;Felipe Garc'ia-Ramos;Hanfeng Li
中科院分区：
文献类型：
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作者：
S. Barbieri;Felipe Garc'ia-Ramos;Hanfeng Li
我们提供了一个统一的方法，它将Lind和Schmidt，Chung和Li关于代数作用的结果与Meyerovitch的一个拓扑结果联系起来，该拓扑结果将熵与渐近对集联系起来。为此，我们引入了一系列马尔可夫性质，并在它们被满足的假设下，证明了拓扑熵和渐近对(代数情况下的同宿群)之间的几个结果。作为我们方法的新应用，我们利用独立熵对的语言，给出了(1)任何上界在有限子群阶上的初等顺从群或(2)任何左可序顺从群的有限表示扩张代数作用的同宿群的特征。
We provide a unifying approach which links results on algebraic actions by Lind and Schmidt, Chung and Li, and a topological result by Meyerovitch that relates entropy to the set of asymptotic pairs. In order to do this we introduce a series of Markovian properties and, under the assumption that they are satisfied, we prove several results that relate topological entropy and asymptotic pairs (the homoclinic group in the algebraic case). As new applications of our method, we give a characterization of the homoclinic group of any finitely presented expansive algebraic action of (1) any elementary amenable group with an upper bound on the orders of finite subgroups or (2) any left orderable amenable group, using the language of independence entropy pairs.