Mandelpinski necklaces in the parameter planes of rational maps

DOI10.1007/978-981-16-0174-3_7zbMath1487.37056OpenAlexW3204476216MaRDI QIDQ2067324

Sebastian M. Marotta, Robert L. Devaney

Publication date: 18 January 2022

Full work available at URL: https://doi.org/10.1007/978-981-16-0174-3_7

zbMATH Keywords

critical pointJulia setcritical valueMandelpinski necklaceMcMullen domainSierpinski holes

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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• Generalized rings around the McMullen domain
• Simple Mandelpinski Necklaces for $$z^2 + \lambda /z^2$$ z 2 + λ / z 2
• Topological characterization of the Sierpiński curve
• The escape trichotomy for singularly perturbed rational maps
• The McMullen domain: Rings around the boundary
• Geometry and Dynamics of Quadratic Rational Maps
• Generalized baby Mandelbrot sets adorned with halos in families of rational maps
• Julia sets converging to the unit disk
• The McMullen domain: Satellite Mandelbrot sets and Sierpinski holes
• 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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