Computational Methods and Function Theory

, Volume 14, Issue 2–3, pp 209–218 | Cite as

The Julia Set and the Fast Escaping Set of a Quasiregular Mapping

  • Walter Bergweiler
  • Alastair Fletcher
  • Daniel A. Nicks
Article

Abstract

It is shown that for quasiregular maps of positive lower order, the Julia set coincides with the boundary of the fast escaping set.

Keywords

Quasiregular mapping Iteration Dynamics Julia set  Fast escaping set 

Mathematics Subject Classification (2000)

Primary 37F10 Secondary 30C65 30D05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Walter Bergweiler
    • 1
  • Alastair Fletcher
    • 2
  • Daniel A. Nicks
    • 3
  1. 1.Mathematisches SeminarChristian-Albrechts-Universität zu KielKielGermany
  2. 2.Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA
  3. 3.School of Mathematical SciencesUniversity of NottinghamNottinghamUK

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