The escaping set of a quasiregular mapping

Bergweiler, W., Fletcher, A., Langley, J. and Meyer, J. (2009) The escaping set of a quasiregular mapping. Proceedings of the American Mathematical Society, 137, pp. 641-651.

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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:Articles
Glasgow Author(s) Enlighten ID:Fletcher, Dr Alastair
Authors: Bergweiler, W., Fletcher, A., Langley, J., and Meyer, J.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Proceedings of the American Mathematical Society
Journal Abbr.:Proc. Amer. Math. Soc.
ISSN (Online):1088-6826

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