The Hilbert cube contains a minimal subshift of full mean dimension
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866917590978265088 |
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| author | Jin, Lei Qiao, Yixiao |
| author_facet | Jin, Lei Qiao, Yixiao |
| contents | We construct a minimal dynamical system of mean dimension equal to $1$, which can be embedded in the shift action on the Hilbert cube $[0,1]^\mathbb{Z}$. This clarifies a seemingly plausible impression about embedding possibility in relation to mean dimension. Our result finally leads to a full understanding of a pair of exact ranges of all the possible values of mean dimension, within which there will always be a minimal dynamical system that can/cannot be embedded in the shift action on the Hilbert cube. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_10339 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Hilbert cube contains a minimal subshift of full mean dimension Jin, Lei Qiao, Yixiao Dynamical Systems We construct a minimal dynamical system of mean dimension equal to $1$, which can be embedded in the shift action on the Hilbert cube $[0,1]^\mathbb{Z}$. This clarifies a seemingly plausible impression about embedding possibility in relation to mean dimension. Our result finally leads to a full understanding of a pair of exact ranges of all the possible values of mean dimension, within which there will always be a minimal dynamical system that can/cannot be embedded in the shift action on the Hilbert cube. |
| title | The Hilbert cube contains a minimal subshift of full mean dimension |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2102.10339 |