Abstract 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.

中文翻译：

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适合群体行动的序列熵和平均序列维度

摘要 设G为连续作用于紧可度量空间X的无限离散可数服从群，Ω为G中的一个序列。利用X的开覆盖，定义了拓扑不变量，即拓扑序列熵。结果表明，拓扑序列熵也可以通过相对生成集或相对分离集来定义。我们证明拓扑序列熵等于拓扑熵乘以常数 K (Ω) 仅取决于序列 Ω。定义了测度论序列熵的概念。这两个序列熵通过变分原理相关。定义了平均拓扑序列维数。只有当拓扑序列熵是无穷大时，它才会是非零的。