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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2310.03194 |
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| _version_ | 1866929213882236928 |
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| author | Huo, Qiang Yuan, Rong |
| author_facet | Huo, Qiang Yuan, Rong |
| contents | In this paper, we introduce mean dimension and rate distortion dimension for $\mathbb{Z}^{k}$-actions dynamical system $(\mathcal{X},\mathbb{Z}^k,T)$. Suppose $(\mathcal{X},\mathbb{Z}^k,T)$ has the marker property. Taking these two variables, the metric $d$ on $\mathcal{X}$ and $\mathbb{Z}^{k}$-invariant measure $μ$, into consideration, a minimax-type variational principle for mean dimension of $\mathbb{Z}^{k}$-actions is established. This result extends the double variational principle obtained recently by Lindenstrauss and Tsukamoto \cite{LT19} from $\mathbb{Z}$-actions dynamical systems to $\mathbb{Z}^{k}$-actions dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03194 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Double variational principle for mean dimension of $\mathbb{Z}^{K}$-actions Huo, Qiang Yuan, Rong Dynamical Systems In this paper, we introduce mean dimension and rate distortion dimension for $\mathbb{Z}^{k}$-actions dynamical system $(\mathcal{X},\mathbb{Z}^k,T)$. Suppose $(\mathcal{X},\mathbb{Z}^k,T)$ has the marker property. Taking these two variables, the metric $d$ on $\mathcal{X}$ and $\mathbb{Z}^{k}$-invariant measure $μ$, into consideration, a minimax-type variational principle for mean dimension of $\mathbb{Z}^{k}$-actions is established. This result extends the double variational principle obtained recently by Lindenstrauss and Tsukamoto \cite{LT19} from $\mathbb{Z}$-actions dynamical systems to $\mathbb{Z}^{k}$-actions dynamical systems. |
| title | Double variational principle for mean dimension of $\mathbb{Z}^{K}$-actions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2310.03194 |