Variational principles of metric mean dimension for random dynamical systems

Fuente: arXiv
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Main Authors: Wang, Yunping, Chen, Ercai, Yang, Kexiang
Format: Preprint
Published: 2023
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author Wang, Yunping
Chen, Ercai
Yang, Kexiang
author_facet Wang, Yunping
Chen, Ercai
Yang, Kexiang
contents 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 $ε$-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.
format Preprint
id arxiv_https___arxiv_org_abs_2310_16461
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Variational principles of metric mean dimension for random dynamical systems
Wang, Yunping
Chen, Ercai
Yang, Kexiang
Dynamical Systems
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 $ε$-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.
title Variational principles of metric mean dimension for random dynamical systems
topic Dynamical Systems
url https://arxiv.org/abs/2310.16461