Böttcher coordinates at superattracting fixed points of holomorphic skew products

Abstract

Let $f:({\mathbb{C}}^2,0)\to ({\mathbb{C}}^2,0)$ be a germ of holomorphic skew product with a superattracting fixed point at the origin. If it has a suitable weight, then we can construct a Böttcher coordinate which conjugates $f$ to the associated monomial map. This Böttcher coordinate is defined on an open set whose interior or boundary contains the origin.

arXiv comment15 pages