A construction of Bottcher coordinates for holomorphic skew products

摘要

Let f(z, w) = (p(z), q(z, w)) be a holomorphic skew product with a superattracting fixed point at the origin. Under one or two assumptions, we prove that f is conjugate to a monomial map on an invariant open set whose closure contains the origin. The monomial map and the open set are determined by the degree of p and the Newton polygon of q.