Minimal subshifts of prescribed mean dimension over general alphabets
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913620470792192 |
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| author | Wang, Xiangtong Zhao, Hang |
| author_facet | Wang, Xiangtong Zhao, Hang |
| contents | Let $G$ be a countable infinite amenable group, $K$ a finite-dimensional compact metrizable space, and $(K^G,σ)$ the full $G$-shift on $K^G$. For any $r\in [0,{\rm mdim}(K^G,σ))$, we construct a minimal subshift $(X,σ)$ of $(K^G,σ)$ with mdim$(X,σ)=r$. Furthermore, we construct a subshift of $([0,1]^G,σ)$ such that its mean dimension is $1$, and that the set of all attainable values of the mean dimension of its minimal subsystems is exactly the interval $[0,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15281 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal subshifts of prescribed mean dimension over general alphabets Wang, Xiangtong Zhao, Hang Dynamical Systems 37B05, 54F45 Let $G$ be a countable infinite amenable group, $K$ a finite-dimensional compact metrizable space, and $(K^G,σ)$ the full $G$-shift on $K^G$. For any $r\in [0,{\rm mdim}(K^G,σ))$, we construct a minimal subshift $(X,σ)$ of $(K^G,σ)$ with mdim$(X,σ)=r$. Furthermore, we construct a subshift of $([0,1]^G,σ)$ such that its mean dimension is $1$, and that the set of all attainable values of the mean dimension of its minimal subsystems is exactly the interval $[0,1)$. |
| title | Minimal subshifts of prescribed mean dimension over general alphabets |
| topic | Dynamical Systems 37B05, 54F45 |
| url | https://arxiv.org/abs/2412.15281 |