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- W2949262700 abstract "This article concerns the iteration of quasiregular mappings on $mathbb{R}^d$ and entire functions on $mathbb{C}$. 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 $f:mathbb{R}^dtomathbb{R}^d$ 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 $f^n$ 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 $|f^n(x)|$ is asymptotic to the iterated maximum modulus $M^n(R,f)$." @default.
- W2949262700 created "2019-06-27" @default.
- W2949262700 creator A5059716211 @default.
- W2949262700 date "2015-11-05" @default.
- W2949262700 modified "2023-09-27" @default.
- W2949262700 title "Slow escaping points of quasiregular mappings" @default.
- W2949262700 hasPublicationYear "2015" @default.
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