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On the iteration of quasimeromorphic mappings

Published online by Cambridge University Press:  06 July 2018

LUKE WARREN
LUKE WARREN*
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD. e-mail: luke.warren@nottingham.ac.uk
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Abstract

The Fatou–Julia theory for rational functions has been extended both to transcendental meromorphic functions and more recently to several different types of quasiregular mappings in higher dimensions. We extend the iterative theory to quasimeromorphic mappings with an essential singularity at infinity and at least one pole, constructing the Julia set for these maps. We show that this Julia set shares many properties with those for transcendental meromorphic functions and for quasiregular mappings of punctured space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 1 , January 2020 , pp. 1 - 11
Copyright
Copyright © Cambridge Philosophical Society 2018 

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References

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