On the capacity dimensions of the Brjuno and Perez-Marco sets

Nurali Akramov, Abduvahhob Ashirov

In this work, we prove that the complement of the Brjuno set $\mathcal{B}$ has a zero capacity with respect to the kernel $k^1_σ(z,ξ)=\ln^2{|z-ξ|}\left|\ln{\ln{\left(e+\frac{1}{|z-…