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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2511.04419 |
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| _version_ | 1866914140999647232 |
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| author | Huang, Wen Tan, Maoru Xu, Leiye |
| author_facet | Huang, Wen Tan, Maoru Xu, Leiye |
| contents | In this paper, we introduce topological dynamical systems with almost countable spectrum. We prove that the Logarithmic Sarnak Conjecture holds for zero-entropy topological dynamical systems whose spectrum is almost countable. This class includes Anzai skew product on $\mathbb{T}^2$ over a rotation of $\mathbb{T}^1$, time-one maps of continuous suspension flows over rotations, systems with finite maximal pattern entropy, and bounded tame systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04419 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almost Countable Spectrum and Logarithmic Sarnak Conjecture Huang, Wen Tan, Maoru Xu, Leiye Dynamical Systems In this paper, we introduce topological dynamical systems with almost countable spectrum. We prove that the Logarithmic Sarnak Conjecture holds for zero-entropy topological dynamical systems whose spectrum is almost countable. This class includes Anzai skew product on $\mathbb{T}^2$ over a rotation of $\mathbb{T}^1$, time-one maps of continuous suspension flows over rotations, systems with finite maximal pattern entropy, and bounded tame systems. |
| title | Almost Countable Spectrum and Logarithmic Sarnak Conjecture |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.04419 |