Slow escaping points of quasiregular mappings

  title={Slow escaping points of quasiregular mappings},
  author={Daniel A. Nicks},
This article concerns the iteration of quasiregular mappings on R 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 : R → R 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… CONTINUE READING

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