Fatou-Julia theory for non-uniformly quasiregular maps

Abstract

Many results of the Fatou-Julia iteration theory of rational functions extend to uniformly quasiregular maps in higher dimensions. We obtain results of this type for certain classes of quasiregular maps which are not uniformly quasiregular.

24 pages

References in corpus (3)

• The escaping set of a quasiregular mapping
• Dynamics of a higher dimensional analog of the trigonometric functions
• Julia sets of uniformly quasiregular mappings are uniformly perfect

Cited by in corpus (11)

• Multifractal analysis of the irregular set for almost-additive sequences via large deviations
• Foundations for an iteration theory of entire quasiregular maps
• The fast escaping set for quasiregular mappings
• Superattracting fixed points of quasiregular mappings
• The size and topology of quasi-Fatou components of quasiregular maps
• Hollow quasi-Fatou components of quasiregular maps
• The Julia set and the fast escaping set of a quasiregular mapping
• The bungee set in quasiregular dynamics
• The escaping set in transcendental dynamics
• Hausdorff dimension in quasiregular dynamics
• On slow escaping and non-escaping points of quasimeromorphic mappings