Böttcher coordinates at superattracting fixed points of holomorphic skew products

Kohei Ueno

Published 2014-12-06Version 1

Let $f : (\mathbf{C}^2, 0) \to (\mathbf{C}^2, 0)$ 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 B\"ottcher coordinate which conjugates $f$ to the associated monomial map. This B\"ottcher coordinate is defined on an open set whose interior or boundary contains the origin.