Wandering domains in quasiregular dynamics
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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.References
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Additional Information
- Daniel A. Nicks
- Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- MR Author ID: 862157
- Email: dan.nicks@nottingham.ac.uk
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1385-1392
- MSC (2010): Primary 30C62, 30C65, 37F50; Secondary 37F10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11625-9
- MathSciNet review: 3008885