标题： 随机动力系统的度量均维变分原理 显示英文标题

标题： Variational principles of metric mean dimension for random dynamical systems

摘要： 众所周知，Bogenschutz和Kifer建立的相对变分原理将纤维拓扑熵和纤维测度论熵联系起来。在随机动力系统背景下，度量均维被引入以表征无限纤维熵系统。我们给出了四种类型的测度论$\epsilon$-熵，称为分割直径递减的测度论熵、Shapira熵、Katok熵和Brin-Katok局部熵，并为度量均维建立了四个变分原理。 显示英文摘要

摘要： It is well-known that the relativized variational principle established by Bogenschutz and Kifer connects the fiber topological entropy and fiber measure-theoretic entropy. In context of random dynamical systems, metric mean dimension was introduced to characterize infinite fiber entropy systems. We give four types of measure-theoretic $\epsilon$-entropies, called measure-theoretic entropy of partitions decreasing in diameter, Shapira's entropy, Katok's entropy and Brin-Katok local entropy, and establish four variational principles for metric mean dimension.