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On Quasiregular Linearizers

On Quasiregular Linearizers Linearization is a well-known concept in complex dynamics. If $$p$$ p is a polynomial and $$z_0$$ z 0 is a repelling fixed point, then there is an entire function $$L$$ L which conjugates $$p$$ p to the linear map $$z\mapsto p^{\prime }(z_0)z$$ z ↦ p ′ ( z 0 ) z . This notion of linearization carries over into the quasiregular setting, in the context of repelling fixed points of uniformly quasiregular mappings. In this article, we investigate how linearizers arising from the same uqr mapping and the same repelling fixed point are related. In particular, any linearizer arising from a uqr solution to a Schröder equation is shown to be automorphic with respect to some quasiconformal group. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-014-0100-0
Publisher site
See Article on Publisher Site

Abstract

Linearization is a well-known concept in complex dynamics. If $$p$$ p is a polynomial and $$z_0$$ z 0 is a repelling fixed point, then there is an entire function $$L$$ L which conjugates $$p$$ p to the linear map $$z\mapsto p^{\prime }(z_0)z$$ z ↦ p ′ ( z 0 ) z . This notion of linearization carries over into the quasiregular setting, in the context of repelling fixed points of uniformly quasiregular mappings. In this article, we investigate how linearizers arising from the same uqr mapping and the same repelling fixed point are related. In particular, any linearizer arising from a uqr solution to a Schröder equation is shown to be automorphic with respect to some quasiconformal group.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jan 8, 2015

References