The Moebius function and continuous extensions of rotations

Joanna Kułaga-Przymus, Mariusz Lemańczyk

Let $f:\mathbb{T}\to \mathbb{R}$ be of class $C^{1+\delta }$ for some $\delta >0$ and let $c\in \mathbb{Z}$. We show that for a generic $\alpha \in \mathbb{R}$, the extension $T_{c,f}\colon \mat…