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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Böttcher coordinates at superattracting fixed points of holomorphic skew products
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by Kohei Ueno PDF
Conform. Geom. Dyn. 20 (2016), 43-57 Request permission

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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Additional Information
  • Kohei Ueno
  • Affiliation: Daido University, Nagoya 457-8530, Japan
  • MR Author ID: 818455
  • Email: k-ueno@daido-it.ac.jp
  • 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
  • © Copyright 2016 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 20 (2016), 43-57
  • MSC (2010): Primary 32H50
  • DOI: https://doi.org/10.1090/ecgd/290
  • MathSciNet review: 3475294