Capacity dimension of the Brjuno set in ${\mathbb{C}}^n$

Nurali Akramov, Karim Rakhimov

In this work, we prove that the complement of the Brjuno set in ${\mathbb{C}}^n$ has zero $C_{\sigma }$-capacity with respect to the kernel $k_{\sigma }(z,\xi )=\Vert z-\xi {\Vert }^{-2n+2}|\log \Vert z-\xi \Vert {|}^{\sigma }$ for an…