On slow escaping and non-escaping points of quasimeromorphic mappings

@inproceedings{Warren2019OnSE,
  title={On slow escaping and non-escaping points of quasimeromorphic mappings},
  author={L. Patrick Warren},
  year={2019}
}
We show that for any quasimeromorphic mapping with an essential singularity at infinity, there exist points whose iterates tend to infinity arbitrarily slowly. This extends a result by Nicks for quasiregular mappings, and Rippon and Stallard for transcendental meromorphic functions on the complex plane. We further establish a new result for the growth rate of quasiregular mappings near an essential singularity, and briefly extend some results regarding the bounded orbit set and the bungee set… CONTINUE READING
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