Sequence entropies and mean sequence dimension for amenable group actions
Sequence entropies and mean sequence dimension for amenable group actions
复制标题
顺从群体行动的序列熵和平均序列维数
DOI：
10.1016/j.jde.2020.06.054
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发表时间：
2020
影响因子：
2.4
通讯作者：
Changrong Zhu
中科院分区：
文献类型：
--
作者：
Junming Gao;Huang Xiaojun;Changrong Zhu
设G是连续作用在紧度量空间X上的无限离散可数可数群，Ω是G中的一个序列，利用X的开覆盖定义了拓扑不变量--拓扑序列熵.证明了拓扑序列熵也可以通过相对生成集或相对分离集来定义。证明了拓扑序列熵等于拓扑熵乘以常数K(Ω)，仅依赖于序列Ω。定义了测度论序列熵的概念。这两个序列熵由变分原理联系在一起。定义了平均拓扑序列维。只有当拓扑序列熵是无穷大时，它才是非零的。
Let G be an infinite discrete countable amenable group acting continuously on a compact metrizable space X and Ω be a sequence in G. By using open covers of X, a topological invariant, the topological sequence entropy, is defined. It is shown that the topological sequence entropy can also be defined through relative spanning set or relative separate set. We prove that the topological sequence entropy equals the topological entropy multiplying a constant K (Ω) depending only on sequence Ω. The notion of the measure-theoretic sequence entropy is defined. The two sequence entropies are related by the variational principle. The mean topological sequence dimension is defined. It will be nonzero only if the topological sequence entropy is infinite.