论文标题
度量平均尺寸
Metric mean dimension of flows
论文作者
论文摘要
本文旨在研究连续流的度量平均维度理论。我们介绍了连续流的度量平均维度的概念，以表征无限拓扑熵的流量的复杂性。对于连续流，我们根据本地$ε$ -Entropy功能和Brin-katok $ε$ -Entropy建立了度量平均维度的变异原理；对于一类称为统一Lipschitz流的特殊流程，我们根据Kolmogorov-Sinai $ε$ -Entropy，Brin-Katok的$ε$ -Entropy和Katok's $ε$ -Entropy建立了公制平均维度的变异原理。
The present paper aims to investigate the metric mean dimension theory of continuous flows. We introduce the notion of metric mean dimension for continuous flows to characterize the complexity of flows with infinite topological entropy. For continuous flows, we establish variational principles for metric mean dimension in terms of local $ε$-entropy function and Brin-Katok $ε$-entropy; For a class of special flow, called uniformly Lipschitz flow, we establish variational principles for metric mean dimension in terms of Kolmogorov-Sinai $ε$-entropy, Brin-Katok's $ε$-entropy and Katok's $ε$-entropy.
