On locally compact groups of small topological entropy
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916141814775808 |
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| author | Russo, Francesco G. Waka, Olwethu |
| author_facet | Russo, Francesco G. Waka, Olwethu |
| contents | We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting behaviour of slender groups. Secondly, we remove the condition of being abelian and consider nilpotent periodic locally compact $p$-groups ($p$ prime), reducing the computations to the case of Sylow $p$-subgroups. Finally, we investigate locally compact Heisenberg $p$-groups $\mathbb{H}_{n}(\mathbb{Q}_{p})$ on the field $\mathbb{Q}_{p}$ of the $p$-adic rationals with $n$ arbitrary positive integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08156 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On locally compact groups of small topological entropy Russo, Francesco G. Waka, Olwethu Group Theory Dynamical Systems General Topology 22A05, 37B40, 54C70 We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting behaviour of slender groups. Secondly, we remove the condition of being abelian and consider nilpotent periodic locally compact $p$-groups ($p$ prime), reducing the computations to the case of Sylow $p$-subgroups. Finally, we investigate locally compact Heisenberg $p$-groups $\mathbb{H}_{n}(\mathbb{Q}_{p})$ on the field $\mathbb{Q}_{p}$ of the $p$-adic rationals with $n$ arbitrary positive integer. |
| title | On locally compact groups of small topological entropy |
| topic | Group Theory Dynamical Systems General Topology 22A05, 37B40, 54C70 |
| url | https://arxiv.org/abs/2304.08156 |