Anosov-Katok constructions for quasi-periodic $\mathrm{SL}(2,R)$ cocycles

Nikolaos Karaliolios, Xu Xu, Qi Zhou

We prove that if the frequency of the quasi-periodic $\mathrm{SL}(2,\mathbb{R})$ cocycle is Diophantine, then the following properties are dense in the subcritical regime: for any $\frac{1…