Sequence entropy and independence in free and minimal actions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910900992081920 |
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| author | Gómez, Jaime León-Torres, Irma Muñoz-López, Víctor |
| author_facet | Gómez, Jaime León-Torres, Irma Muñoz-López, Víctor |
| contents | For every countable infinite group that admits $\mathbb{Z}$ as a homomorphic image, we show that for each $m\in\mathbb{N}$, there exists a minimal action whose topological sequence entropy is $\log(m)$. Furthermore, for every countable infinite group $G$ that contains a finite index normal subgroup $G'$ isomorphic to $\mathbb{Z}^r$, and for every $m\in \mathbb{N}$, we found a free minimal action with topological sequence entropy $\log(n)$, where $m\leq n\leq m^{2^r[G:G']}$. In both cases, we also show that the aforementioned minimal actions admit non-trivial independence tuples of size $n$ but do not admit non-trivial independence tuples of size $n+1$ for some $n\geq m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequence entropy and independence in free and minimal actions Gómez, Jaime León-Torres, Irma Muñoz-López, Víctor Dynamical Systems 37B05 (Primary), 37B10 (Primary), 37B40 (Secondary) For every countable infinite group that admits $\mathbb{Z}$ as a homomorphic image, we show that for each $m\in\mathbb{N}$, there exists a minimal action whose topological sequence entropy is $\log(m)$. Furthermore, for every countable infinite group $G$ that contains a finite index normal subgroup $G'$ isomorphic to $\mathbb{Z}^r$, and for every $m\in \mathbb{N}$, we found a free minimal action with topological sequence entropy $\log(n)$, where $m\leq n\leq m^{2^r[G:G']}$. In both cases, we also show that the aforementioned minimal actions admit non-trivial independence tuples of size $n$ but do not admit non-trivial independence tuples of size $n+1$ for some $n\geq m$. |
| title | Sequence entropy and independence in free and minimal actions |
| topic | Dynamical Systems 37B05 (Primary), 37B10 (Primary), 37B40 (Secondary) |
| url | https://arxiv.org/abs/2504.00960 |