Analysis and Mathematical Physics

, Volume 4, Issue 1–2, pp 83–98 | Cite as

The fast escaping set for quasiregular mappings

  • Walter Bergweiler
  • David Drasin
  • Alastair Fletcher
Article

Abstract

The fast escaping set of a transcendental entire function is the set of all points which tend to infinity under iteration as fast as possible compatible with the growth of the function. We study the analogous set for quasiregular mappings in higher dimensions and show, among other things, that various equivalent definitions of the fast escaping set for transcendental entire functions in the plane also coincide for quasiregular mappings. We also exhibit a class of quasiregular mappings for which the fast escaping set has the structure of a spider’s web.

Mathematics Subject Classification (2000)

Primary 37F10 Secondary 30C65 30D05 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Walter Bergweiler
    • 1
  • David Drasin
    • 2
  • Alastair Fletcher
    • 3
  1. 1.Mathematisches SeminarChristian-Albrechts-Universität zu Kiel KielGermany
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA
  3. 3.Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA

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