Slow escaping points of quasiregular mappings

Nicks, Daniel A. (2016) Slow escaping points of quasiregular mappings. Mathematische Zeitschrift . ISSN 1432-1823

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Abstract

This article concerns the iteration of quasiregular mappings on Rd and entire functions on C. It is shown that there are always points at which the iterates of a quasiregular map tend to infinity at a controlled rate. Moreover, an asymptotic rate of escape result is proved that is new even for transcendental entire functions. Let f:Rd→Rd be quasiregular of transcendental type. Using novel methods of proof, we generalise results of Rippon and Stallard in complex dynamics to show that the Julia set of f contains points at which the iterates fn tend to infinity arbitrarily slowly. We also prove that, for any large R, there is a point x with modulus approximately R such that the growth of |fn(x)| is asymptotic to the iterated maximum modulus Mn(R,f).

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00209-016-1687-9
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s00209-016-1687-9
Depositing User: Eprints, Support
Date Deposited: 19 Jul 2016 08:10
Last Modified: 14 Sep 2016 09:06
URI: http://eprints.nottingham.ac.uk/id/eprint/35154

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