The escaping set of a quasiregular mapping

Abstract

We show that if the maximum modulus of a quasiregular mapping f grows sufficiently rapidly then there exists a non-empty escaping set I(f) consisting of points whose forward orbits under iteration tend to infinity. This set I(f) has an unbounded component but, in contrast to the case of entire functions on the complex plane, the closure of I(f) may have a bounded component.

10 pages

Cited by in corpus (14)

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• Hollow quasi-Fatou components of quasiregular maps
• The size and topology of quasi-Fatou components of quasiregular maps
• The Julia set and the fast escaping set of a quasiregular mapping
• Julia sets of uniformly quasiregular mappings are uniformly perfect
• The bungee set in quasiregular dynamics
• Eremenko's conjecture, wandering Lakes of Wada, and maverick points
• The escaping set in transcendental dynamics
• Permutable Quasiregular Maps
• Hausdorff dimension in quasiregular dynamics
• On slow escaping and non-escaping points of quasimeromorphic mappings