Cantor necklaces and structurally unstable Sierpinski curve Julia sets for rational maps

DOI10.1007/BF02972685zbMath1122.37033OpenAlexW2004091095WikidataQ123148075 ScholiaQ123148075MaRDI QIDQ2457732

Robert L. Devaney

Publication date: 23 October 2007

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02972685

zbMATH Keywords

Cantor setfamilies of rational mapshybrid Sierpinski curvestructurally unstable sets

Mathematics Subject Classification ID

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 (13)

Accessible Mandelbrot sets in the family \(z^n + \lambda /z^n\) ⋮ A Mandelpinski maze for rational maps of the form \(z^n + \lambda / z^d\) ⋮ Fatou components and Julia sets of singularly perturbed rational maps with positive parameter ⋮ Escape components of McMullen maps ⋮ Mandelpinski structures in the parameter planes of rational maps ⋮ A Cantor-Mandelbrot-Sierpiński tree in the parameter plane for rational maps ⋮ Julia sets converging to filled quadratic Julia sets ⋮ On the Hausdorff dimension of the Sierpiński Julia sets ⋮ Julia sets converging to the unit disk ⋮ On the dynamics of the singularly perturbed rational maps ⋮ Mandelpinski spokes in the parameter planes of rational maps ⋮ CHECKERBOARD JULIA SETS FOR RATIONAL MAPS ⋮ Singular perturbations of complex polynomials

Cites Work

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• Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou- Julia problem on wandering domains
• Buried Sierpinski curve Julia sets
• Topological characterization of the Sierpiński curve
• The escape trichotomy for singularly perturbed rational maps
• Geometry and Dynamics of Quadratic Rational Maps
• Symbolic dynamics for a Sierpinski curve Julia set
• Sierpinski-curve Julia sets and singular perturbations of complex polynomials

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