Böttcher coordinates at superattracting fixed points of holomorphic skew products

Ueno, Kohei

doi:10.1090/ecgd/290

Böttcher coordinates at superattracting fixed points of holomorphic skew products
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by Kohei Ueno

Conform. Geom. Dyn. 20 (2016), 43-57

DOI: https://doi.org/10.1090/ecgd/290

Published electronically: March 18, 2016

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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 invariant open set whose interior or boundary contains the origin.

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