Measure complexity and rigid systems
Measure complexity and rigid systems
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测量复杂性和刚性系统
DOI：
10.1007/s10114-021-0179-y
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发表时间：
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通讯作者：
Zhou Xiaomin
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作者：
Huang Wen;Wei Runju;Yu Tao;Zhou Xiaomin
本文引入了两个度量：最大度量Q和平均度量。利用这两个度量给出了刚性保持度量系统的一个等价刻画。证明了拓扑动力系统(X，T)上的不变测度μ关于n_n，q_f有有界复杂性且仅当μ关于有界复杂性当且仅当(X，，μ，T)是刚性的。我们还得到了遍历保测系统的测度论熵的计算公式。拓扑动力系统的拓扑熵)由两个度量Dn，Q和。
In this paper we introduce two metrics: the max metricdn,qand the mean metric. We give an equivalent characterization of rigid measure preserving systems by the two metrics. It turns out that an invariant measureμon a topological dynamical system (X, T) has bounded complexity with respect todn,qif and only ifμhas bounded complexity with respect toif and only if (X,,μ, T) is rigid. We also obtain computation formulas of the measure-theoretic entropy of an ergodic measure preserving system (resp. the topological entropy of a topological dynamical system) by the two metricsdn,qand.