Ergodic measures in minimal group actions with finite topological sequence entropy
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911761627611136 |
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| author | Liu, Chunlin Wang, Xiangtong Xu, Leiye |
| author_facet | Liu, Chunlin Wang, Xiangtong Xu, Leiye |
| contents | Let $G$ be an infinite discrete countable group and $(X,G)$ be a minimal $G$-system. In this paper, we prove the supremum of topological sequence entropy of $(X,G)$ is not less than $\log(\sum_{μ\in\mathcal{M}^e(X,G)}e^{h_μ^*(X,G)})$. If additionally $G$ is abelian then there is a constant $K\in\mathbb{N}\cup\{\infty\}$ with $\log K\le h_{top}^*(X,G)$ such that $ν(\{y\in H:|π^{-1}(y)|=K\})=1$ where $(H,G)$ is the maximal equicontinuous factor of $(X,G)$, $π:(X,G)\to (H,G)$ is the factor map and $ν$ is the Haar measure of $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03976 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ergodic measures in minimal group actions with finite topological sequence entropy Liu, Chunlin Wang, Xiangtong Xu, Leiye Dynamical Systems Let $G$ be an infinite discrete countable group and $(X,G)$ be a minimal $G$-system. In this paper, we prove the supremum of topological sequence entropy of $(X,G)$ is not less than $\log(\sum_{μ\in\mathcal{M}^e(X,G)}e^{h_μ^*(X,G)})$. If additionally $G$ is abelian then there is a constant $K\in\mathbb{N}\cup\{\infty\}$ with $\log K\le h_{top}^*(X,G)$ such that $ν(\{y\in H:|π^{-1}(y)|=K\})=1$ where $(H,G)$ is the maximal equicontinuous factor of $(X,G)$, $π:(X,G)\to (H,G)$ is the factor map and $ν$ is the Haar measure of $H$. |
| title | Ergodic measures in minimal group actions with finite topological sequence entropy |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2312.03976 |