Quasisymmetries of Sierpiński carpet Julia sets

DOI10.1016/J.AIM.2016.06.007zbMath1358.37083arXiv1403.0392OpenAlexW2962732259WikidataQ121365145 ScholiaQ121365145MaRDI QIDQ305723

Mario Bonk, Sergei Merenkov, Mikhail Lyubich

Publication date: 30 August 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.0392

zbMATH Keywords

Julia setsrational mapsSierpiński carpets

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (16)

A characterization of Sierpiński carpet rational maps ⋮ Quasisymmetrically co-Hopfian Menger curves and Sierpiński spaces ⋮ On the Hausdorff dimension of the residual set of a packing by smooth curves ⋮ Square Sierpiński carpets and Lattès maps ⋮ A criterion to generate carpet Julia sets ⋮ Semi-hyperbolic rational maps and size of Fatou components ⋮ Quasisymmetric geometry of Sierpiński carpet Julia sets ⋮ On the dynamics of a family of singularly perturbed rational maps ⋮ Quasispheres and metric doubling measures ⋮ Invariant Jordan curves of Sierpiński carpet rational maps ⋮ Quasisymmetric geometry of the Julia sets of McMullen maps ⋮ Quasisymmetries of the basilica and the Thompson group ⋮ Area and Hausdorff dimension of Sierpiński carpet Julia sets ⋮ Quasisymmetric uniformization and Hausdorff dimensions of Cantor circle Julia sets ⋮ On dynamical gaskets generated by rational maps, Kleinian groups, and Schwarz reflections ⋮ Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps

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