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The escaping set of a quasiregular mapping
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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. ISSN 0002-9939
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Official URL: http://dx.doi.org/10.1090/S0002-9939-08-09609-3
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 > Mathematics |
| Journal or Publication Title: | Proceedings of the American Mathematical Society |
| Publisher: | American Mathematical Society |
| ISSN: | 0002-9939 |
| Date: | February 2008 |
| Volume: | Vol.137 |
| Number: | No.2 |
| Number of Pages: | 11 |
| Page Range: | pp. 641-651 |
| Identification Number: | 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 |
| URI: | http://wrap.warwick.ac.uk/id/eprint/48360 |
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