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arXiv · 1412.2202

Böttcher coordinates at superattracting fixed points of holomorphic skew products

Kohei Ueno
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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 open set whose interior or boundary contains the origin.

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Kohei Ueno. 2015-10-09. Böttcher coordinates at superattracting fixed points of holomorphic skew products. https://arxiv.org/abs/1412.2202

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