Fatou–Julia theory for non-uniformly quasiregular maps

DOI10.1017/S0143385711000915zbMath1279.37037arXiv1102.1910OpenAlexW3101675528WikidataQ121454213 ScholiaQ121454213MaRDI QIDQ4911061

Walter Bergweiler

Publication date: 13 March 2013

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.1910

zbMATH Keywords

quasiregular mapsFatou-Julia iteration theorynon-uniformly maps

Mathematics Subject Classification ID

Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50)

Related Items (19)

Julia sets of Zorich maps ⋮ On Julia limiting directions in higher dimensions ⋮ The size and topology of quasi-Fatou components of quasiregular maps ⋮ Periodic domains of quasiregular maps ⋮ Slow escaping points of quasiregular mappings ⋮ Permutable quasiregular maps ⋮ Explosion points and topology of Julia sets of Zorich maps ⋮ The fast escaping set for quasiregular mappings ⋮ Foundations for an iteration theory of entire quasiregular maps ⋮ Strongly automorphic mappings and Julia sets of uniformly quasiregular mappings ⋮ The Julia set and the fast escaping set of a quasiregular mapping ⋮ Hollow quasi-Fatou components of quasiregular maps ⋮ Fixed curves near fixed points ⋮ On the iteration of quasimeromorphic mappings ⋮ Superattracting fixed points of quasiregular mappings ⋮ Dynamics of quasiregular mappings with constant complex dilatation ⋮ On slow escaping and non-escaping points of quasimeromorphic mappings ⋮ The dynamics of quasiregular maps of punctured space ⋮ Poincaré linearizers in higher dimensions

Cites Work

• Unnamed Item
• Karpińska's paradox in dimension 3
• Iteration of quasiregular mappings
• Averages of the counting function of a quasiregular mapping
• On the number of omitted values of entire quasiregular mappings
• Conformal geometry and quasiregular mappings
• Metrical characterization of conformal capacity zero
• Quasirational dynamic system
• The analogue of Picard's theorem for quasiregular mappings in dimension three
• Dynamics of a higher dimensional analog of the trigonometric functions
• Quasiregular dynamics on the n-sphere
• The escaping set of a quasiregular mapping
• A Heuristic Principle in Complex Function Theory
• A remark on domains quasiconformally equivalent to a ball
• On the iteration of rational functions
• Branch sets of uniformly quasiregular maps
• Uniformly quasiregular mappings of Lattès type
• Local dynamics of uniformly quasiregular mappings

This page was built for publication: Fatou–Julia theory for non-uniformly quasiregular maps