Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Huang, Wen, Tan, Maoru, Xu, Leiye
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G402512718, G7210056353, G8659864915
OpenAlex ID: W4416025977
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