Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Wandering domains in quasiregular dynamics
HTML articles powered by AMS MathViewer

by Daniel A. Nicks PDF
Proc. Amer. Math. Soc. 141 (2013), 1385-1392 Request permission

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
Similar Articles
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