A construction of Böttcher coordinates for holomorphic skew products

Abstract

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 $q$.

arXiv comment25 pages

References in corpus (1)

• Fatou components of elliptic polynomial skew products

Cited by in corpus (1)

• Attraction rates for iterates of a superattracting skew product