Möbius disjointness for $C^{1+\epsilon }$ skew products

Abstract

We show that for $\epsilon >0$, every $C^{1+\epsilon }$ skew product on ${\mathbb{T}}^2$ over a rotation of ${\mathbb{T}}^1$ satisfies Sarnak's conjecture. This is an improvement of earlier results of Kulaga-Przymus-Lemańczyk, Huang-Wang-Ye, and Kanigowski-Lemańczyk-Radziwill.

16 pages. To appear in IMRN

References in corpus (3)

• Möbius disjointness for homogeneous dynamics
• Möbius disjointness for non-uniquely ergodic skew products
• Centralizer and liftable centralizer of special flows over rotations