Bohr chaoticity of principal algebraic actions and Riesz product measures
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| author | Fan, Aihua Schmidt, Klaus Verbitskiy, Evgeny |
| author_facet | Fan, Aihua Schmidt, Klaus Verbitskiy, Evgeny |
| contents | For a continuous $\mathbb{N}^d$ or $\mathbb{Z}^d$ action on a compact space, we introduce the notion of Bohr chaoticity, which is an invariant of topological conjugacy and which is proved stronger than having positive entropy. We prove that all principal algebraic $\mathbb{Z}$ actions of positive entropy are Bohr-chaotic. The same is proved for principal algebraic $\mathbb{Z}^d$ ($d\ge 2$) actions of positive entropy under the condition of existence of summable homoclinic points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_04767 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bohr chaoticity of principal algebraic actions and Riesz product measures Fan, Aihua Schmidt, Klaus Verbitskiy, Evgeny Dynamical Systems 37B02, 42A55 For a continuous $\mathbb{N}^d$ or $\mathbb{Z}^d$ action on a compact space, we introduce the notion of Bohr chaoticity, which is an invariant of topological conjugacy and which is proved stronger than having positive entropy. We prove that all principal algebraic $\mathbb{Z}$ actions of positive entropy are Bohr-chaotic. The same is proved for principal algebraic $\mathbb{Z}^d$ ($d\ge 2$) actions of positive entropy under the condition of existence of summable homoclinic points. |
| title | Bohr chaoticity of principal algebraic actions and Riesz product measures |
| topic | Dynamical Systems 37B02, 42A55 |
| url | https://arxiv.org/abs/2103.04767 |