On the dynamics of the singularly perturbed rational maps

DOI10.1007/S10114-010-8073-ZzbMath1205.30024OpenAlexW2120229234MaRDI QIDQ5962263

Lian Rong Ding

Publication date: 21 September 2010

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-010-8073-z

zbMATH Keywords

Julia setFatou setnormal familybifurcation locusattracting cycleSierpinski curve

Mathematics Subject Classification ID

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)

Cites Work

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• Sierpiński curve Julia sets of rational maps
• Complex dynamics
• The buried points on the Julia sets of rational and entire functions
• Cantor necklaces and structurally unstable Sierpinski curve Julia sets for rational maps
• Buried Sierpinski curve Julia sets
• Topological characterization of the Sierpiński curve
• The escape trichotomy for singularly perturbed rational maps
• On the dynamics of the McMullen family 𝑅(𝑧)=𝑧^{𝑚}+𝜆/𝑧^{ℓ}
• Structure of the McMullen domain in the parameter planes for rational maps
• Sierpinski-curve Julia sets and singular perturbations of complex polynomials

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