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 $C_{\ddot{I}}ƒ$-capacity with respect to the kernel $k_{\ddot{I}}ƒ(z,\hat{I}¾)=\Vert z-\hat{I}¾{\Vert }^{-2n+2}|\log \Vert z-\hat{I}¾\Vert {|}^{\ddot{I}}ƒ$…