Variational principles of metric mean dimension for random dynamical systems
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914051534094336 |
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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 |