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Slow escaping points of quasiregular mappings

Nicks, Daniel A.

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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).


Nicks, D. A. (in press). Slow escaping points of quasiregular mappings. Mathematische Zeitschrift,

Journal Article Type Article
Acceptance Date Mar 20, 2016
Online Publication Date May 9, 2016
Deposit Date Jul 19, 2016
Publicly Available Date Jul 19, 2016
Journal Mathematische Zeitschrift
Print ISSN 0025-5874
Electronic ISSN 1432-1823
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Public URL
Publisher URL
Additional Information The final publication is available at Springer via
Contract Date Jul 19, 2016


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