SFT covers for actions of the first Grigorchuk group
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917610284646400 |
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| author | Grigorchuk, Rostislav Salo, Ville |
| author_facet | Grigorchuk, Rostislav Salo, Ville |
| contents | We study symbolic dynamical representations of actions of the first Grigorchuk group $G$, namely its action on the boundary of the infinite rooted binary tree, its representation in the topological full group of a minimal substitutive $\mathbb{Z}$-shift, and its representation as a minimal system of Schreier graphs. We show that the first system admits an SFT cover, and the latter two systems are conjugate to sofic subshifts on $G$, but are not of finite type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06480 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SFT covers for actions of the first Grigorchuk group Grigorchuk, Rostislav Salo, Ville Dynamical Systems Group Theory We study symbolic dynamical representations of actions of the first Grigorchuk group $G$, namely its action on the boundary of the infinite rooted binary tree, its representation in the topological full group of a minimal substitutive $\mathbb{Z}$-shift, and its representation as a minimal system of Schreier graphs. We show that the first system admits an SFT cover, and the latter two systems are conjugate to sofic subshifts on $G$, but are not of finite type. |
| title | SFT covers for actions of the first Grigorchuk group |
| topic | Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2403.06480 |