Asymptotic size of Herman rings of the complex standard family by quantitative quasiconformal surgery
Asymptotic size of Herman rings of the complex standard family by quantitative quasiconformal surgery
In this paper we consider the complexification of the Arnold standard family of circle maps given by $\widetilde F_{\alpha,\epsilon}(u)=ue^{i\alpha} e^{({\epsilon}/{2}) (u-{1}/{u})}$, with $\alpha=\alpha(\epsilon)$ chosen so that $\widetilde F_{\alpha(\epsilon),\epsilon}$ restricted to the unit circle has a prefixed rotation number $\theta$ belonging to the set of Brjuno numbers. In this case, it …