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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Wandering domains in quasiregular dynamics


Author: Daniel A. Nicks
Journal: Proc. Amer. Math. Soc. 141 (2013), 1385-1392
MSC (2010): Primary 30C62, 30C65, 37F50; Secondary 37F10
Published electronically: September 19, 2012
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Abstract: We show that wandering domains can exist in the Fatou set of a polynomial type quasiregular mapping of the plane. We also give an example of a quasiregular mapping of the plane, with an essential singularity at infinity, which has a sequence of wandering domains contained in a bounded part of the plane. This contrasts with the situation in the analytic case, where wandering domains are impossible for polynomials and, for transcendental entire functions, the existence of wandering domains in a bounded part of the plane has been an open problem for many years.


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Additional Information

Daniel A. Nicks
Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
Email: dan.nicks@nottingham.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11625-9
PII: S 0002-9939(2012)11625-9
Received by editor(s): January 7, 2011
Received by editor(s) in revised form: August 23, 2011
Published electronically: September 19, 2012
Communicated by: Mario Bonk
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.