Special Session 45: Frontiers in Topological Dynamics: Theory, Applications, and Interdisciplinary Connections

Almost Countable Spectrum and Logarithmic Sarnak Conjecture
Leiye Xu
University of Science and Technology of China
Peoples Rep of China
Co-Author(s):    Wen Huang and Maoru Tan
Abstract:
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.