Julia sets of uniformly quasiregular mappings are uniformly perfect

DOI10.1017/S0305004111000478zbMath1235.37014arXiv1012.1378OpenAlexW3098675334WikidataQ121864538 ScholiaQ121864538MaRDI QIDQ3095783

Alastair Fletcher, Daniel A. Nicks

Publication date: 4 November 2011

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.1378

zbMATH Keywords

Julia setHausdorff dimensionannulusFatou setquasiregularmodulusuniformly perfectring domain

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (6)

Iteration of quasiregular tangent functions in three dimensions ⋮ Foundations for an iteration theory of entire quasiregular maps ⋮ On uniformly disconnected Julia sets ⋮ Quasiregular semigroups with examples ⋮ Attractor sets and Julia sets in low dimensions ⋮ Poincaré linearizers in higher dimensions

Cites Work

• Iteration of quasiregular mappings
• Conformal geometry and quasiregular mappings
• Uniformly perfect sets and the Poincaré metric
• Quasiregular analogues of critically finite rational functions with parabolic orbifold
• Quasiregular dynamics on the n-sphere
• The escaping set of a quasiregular mapping
• Julia Sets are Uniformly Perfect
• The Poincaré Metric of Plane Domains
• Quasisymmetric embeddings of metric spaces
• Julia sets of rational functions are uniformly perfect
• Uniformly Perfect Sets and Quasiregular Mappings
• Uniformly quasiregular mappings of Lattès type
• Local dynamics of uniformly quasiregular mappings
• An explicit bound for uniform perfectness of the Julia sets of rational maps

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