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arXiv · 1803.10422

A construction of Böttcher coordinates for holomorphic skew products

Kohei Ueno
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Abstract

Let $f(z,w)=(p(z),q(z,w))$ be a holomorphic skew product with a superattracting fixed point at the origin. Under one or two assumptions, we prove that $f$ is conjugate to a monomial map on an invariant open set whose closure contains the origin. The monomial map and the open set are determined by the degree of $p$ and the Newton polygon of $q$.

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Kohei Ueno. 2018-03-28. A construction of Böttcher coordinates for holomorphic skew products. https://doi.org/10.1088/1361-6544%2Fab0914

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