Bergweiler, Walter, Fletcher, Alastair, Langley, Jim and Meyer, Janis (2008) The escaping set of a quasiregular mapping. Proceedings of the American Mathematical Society, Vol.137 (No.2). pp. 641-651. doi:10.1090/S0002-9939-08-09609-3

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Abstract

We show that if the maximum modulus of a quasiregular mapping f : RN → RN grows sufficiently rapidly, then there exists a nonempty escaping set I(f) consisting of points whose forward orbits under iteration of f tend to infinity. We also construct a quasiregular mapping for which the closure of I(f) has a bounded component. This stands in contrast to the situation for entire functions in the complex plane, for which all components of the closure of I(f) are unbounded and where it is in fact conjectured that all components of I(f) are unbounded.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Proceedings of the American Mathematical Society
Publisher:	American Mathematical Society
ISSN:	0002-9939
Official Date:	February 2008
Dates:	Date Event February 2008 Published
Volume:	Vol.137
Number:	No.2
Number of Pages:	11
Page Range:	pp. 641-651
DOI:	10.1090/S0002-9939-08-09609-3
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	German-Israeli Foundation for Scientific Research and Development (GIF), EU Research Training Network CODY, EPSRC, ESF Research Networking Programme HCAA, DFG
Grant number:	G-809-234.6/2003, RA22AP, ME 3198/1-1

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