Attraction rates for iterates of a superattracting skew product

Abstract

Let $f(z,w)=(p(z),q(z,w))$ be a holomorphic skew product with a superattracting fixed point at the origin. In the previous paper we have succeeded to specify a dominant term of $q$ by the order of $p$ and the Newton polygon of $q$ and to construct a B\"{o}ttcher coordinate on an invariant wedge. By using the same idea and terminologies, we give inequalities of attraction rates for the vertical dynamics of $f$ in this paper. The results hold not only for the superattracting case, but for all the other cases.