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arXiv · 1608.02697

Möbius disjointness for non-uniquely ergodic skew products

Zhiren Wang
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Abstract

For $τ>2$, let $T$ be a $C^τ$ skew product map of the form $(x+α,y+h(x))$ on $\mathbb T^2$ over a rotation of the circle. We show that if $T$ preserves a measurable section, then it is disjoint to the Möbius sequence. This in particular implies that any non-uniquely ergodic $C^τ$ skew product map on $\mathbb T^2$ has a finite index factor that is disjoint to the Möbius sequence.

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Zhiren Wang. 2017-09-28. Möbius disjointness for non-uniquely ergodic skew products. https://doi.org/10.1007/s00222-016-0707-z

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