DANIEL NICKS Dan.Nicks@nottingham.ac.uk
Lecturer
Slow escaping points of quasiregular mappings
Nicks, Daniel A.
Authors
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).
Citation
Nicks, D. A. (in press). Slow escaping points of quasiregular mappings. Mathematische Zeitschrift, https://doi.org/10.1007/s00209-016-1687-9
Journal Article Type | Article |
---|---|
Acceptance Date | Mar 20, 2016 |
Online Publication Date | May 9, 2016 |
Deposit Date | Jul 19, 2016 |
Publicly Available Date | Mar 29, 2024 |
Journal | Mathematische Zeitschrift |
Print ISSN | 0025-5874 |
Electronic ISSN | 1432-1823 |
Publisher | Springer Verlag |
Peer Reviewed | Peer Reviewed |
DOI | https://doi.org/10.1007/s00209-016-1687-9 |
Public URL | https://nottingham-repository.worktribe.com/output/790813 |
Publisher URL | http://link.springer.com/article/10.1007%2Fs00209-016-1687-9 |
Additional Information | The final publication is available at Springer via http://dx.doi.org/10.1007/s00209-016-1687-9 |
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