Möbius disjointness for non-uniquely ergodic skew products

Zhiren Wang

For $\tau >2$, let $T$ be a $C^{\tau }$ skew product map of the form $(x+\alpha ,y+h(x))$ on ${\mathbb{T}}^2$ over a rotation of the circle. We show that if $T$ preserves a measurable section, then i…