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Conformal Geometry and Dynamics

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Böttcher coordinates at superattracting fixed points of holomorphic skew products

Author: Kohei Ueno
Journal: Conform. Geom. Dyn. 20 (2016), 43-57
MSC (2010): Primary 32H50
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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Kohei Ueno
Affiliation: Daido University, Nagoya 457-8530, Japan

Keywords: Complex dynamics, B\"ottcher coordinates, skew products
Received by editor(s): April 18, 2015
Received by editor(s) in revised form: December 31, 2015, and January 14, 2016
Published electronically: March 18, 2016
Article copyright: © Copyright 2016 American Mathematical Society