Karpińska's paradox in dimension 3

DOI10.1215/00127094-2010-047zbMath1218.37057arXiv0902.2686OpenAlexW3101934135MaRDI QIDQ605908

Walter Bergweiler

Publication date: 15 November 2010

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.2686

zbMATH Keywords

Julia setsfractal geometrycomplex dynamical systemsquasi-regular self-maps

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) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (15)

Julia sets of Zorich maps ⋮ Periodic domains of quasiregular maps ⋮ Dynamics of generalised exponential maps ⋮ Explosion points and topology of Julia sets of Zorich maps ⋮ The dimension paradox in parameter space of cosine family ⋮ Hausdorff measure of hairs without endpoints in the exponential family ⋮ Escape rate and Hausdorff measure for entire functions ⋮ The fast escaping set for quasiregular mappings ⋮ Foundations for an iteration theory of entire quasiregular maps ⋮ Quasiregular mappings of polynomial type in ℝ² ⋮ Fatou–Julia theory for non-uniformly quasiregular maps ⋮ Strongly automorphic mappings and Julia sets of uniformly quasiregular mappings ⋮ The Julia set and the fast escaping set of a quasiregular mapping ⋮ Non-escaping points of Zorich maps ⋮ On the differentiability of hairs for Zorich maps

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