The fast escaping set for quasiregular mappings

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 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.

13 pages

References in corpus (7)

• Fast escaping points of entire functions
• Dynamics of meromorphic functions with direct or logarithmic singularities
• The escaping set of a quasiregular mapping
• Karpińska's paradox in dimension three
• Fatou-Julia theory for non-uniformly quasiregular maps
• The structure of spider's web fast escaping sets
• Poincaré functions with spiders' webs

Cited by in corpus (9)

• Superattracting fixed points of quasiregular mappings
• Hollow quasi-Fatou components of quasiregular maps
• The size and topology of quasi-Fatou components of quasiregular maps
• 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