Böttcher coordinates at superattracting fixed points of holomorphic skew products

Abstract

Let f : ( C 2 , 0 ) → ( C 2 , 0 ) 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 f to the associated monomial map. This Böttcher coordinate is defined on an invariant open set whose interior or boundary contains the origin.