Sierpiński curve Julia sets of rational maps

DOI10.1007/BF03321617zbMath1113.37027WikidataQ122927972 ScholiaQ122927972MaRDI QIDQ879656

Norbert Steinmetz

Publication date: 14 May 2007

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

zbMATH Keywords

quasiconformal mappingMandelbrot setMcMullen familyquasiconjugationSierpiński hole

Mathematics Subject Classification ID

Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (9)

RINGS AROUND SIERPINSKI HOLES ⋮ Fatou components and Julia sets of singularly perturbed rational maps with positive parameter ⋮ Generalized rings around the McMullen domain ⋮ On the dynamics of the rational family \(f_{t}(z)={-t/4} {(z^{2}-2)^{2}/(z^{2}-1)}\) ⋮ On the dynamics of rational maps with two free critical points ⋮ On the dynamics of the singularly perturbed rational maps ⋮ Relating singularly perturbed rational maps to families of entire maps ⋮ Singular perturbations of complex polynomials ⋮ On the dynamics of the McMullen family 𝑅(𝑧)=𝑧^{𝑚}+𝜆/𝑧^{ℓ}

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• Structure of the McMullen domain in the parameter planes for rational maps
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