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Poincaré linearizers in higher dimensions


Author: Alastair Fletcher
Journal: Proc. Amer. Math. Soc. 143 (2015), 2543-2557
MSC (2010): Primary 37F10; Secondary 30C65, 30D05
Published electronically: February 16, 2015
MathSciNet review: 3326035
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Abstract: It is well-known that a holomorphic function near a repelling fixed point may be conjugated to a linear function. The function which conjugates is called a Poincaré linearizer and may be extended to a transcendental entire function in the plane. In this paper, we study the dynamics of a higher dimensional generalization of Poincaré linearizers. These arise by conjugating a uniformly quasiregular mapping in $ \mathbb{R}^m$ near a repelling fixed point to the mapping $ x\mapsto 2x$. In particular, we show that the fast escaping set of such a linearizer has a spider's web structure.


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Additional Information

Alastair Fletcher
Affiliation: Department of Mathematics, Northern Illinois University, Dekalb, IL 60115
Email: fletcher@math.niu.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12462-8
Received by editor(s): August 23, 2013
Received by editor(s) in revised form: January 16, 2014
Published electronically: February 16, 2015
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2015 American Mathematical Society