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Quasiregular dynamics on the n-sphere

Published online by Cambridge University Press:  18 January 2010

ALASTAIR N. FLETCHER  and
DANIEL A. NICKS
ALASTAIR N. FLETCHER
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (email: [email protected])
DANIEL A. NICKS
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK (email: [email protected])
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Abstract

In this paper, we investigate the boundary of the escaping set I(f) for quasiregular mappings on ℝn, both in the uniformly quasiregular case and in the polynomial type case. The aim is to show that ∂I(f) is the Julia set J(f) when the latter is defined, and shares properties with the Julia set when J(f) is not defined.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 1 , February 2011 , pp. 23 - 31
Copyright
Copyright © Cambridge University Press 2009

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