The McMullen domain: Rings around the boundary

DOI10.1090/S0002-9947-07-04137-2zbMath1109.37038MaRDI QIDQ3431213

Sebastian M. Marotta, Robert L. Devaney

Publication date: 5 April 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Julia setsbasin of attractioncritical pointsCantor setMandelbrot setrational mapsSierpinski holesproperties of parameter planerings in dynamical planeSierpinski curves

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 (16)

RINGS AROUND SIERPINSKI HOLES ⋮ Accessible Mandelbrot sets in the family \(z^n + \lambda /z^n\) ⋮ A GENERALIZED VERSION OF THE MCMULLEN DOMAIN ⋮ Escape components of McMullen maps ⋮ Simple Mandelpinski Necklaces for $$z^2 + \lambda /z^2$$ z 2 + λ / z 2 ⋮ Generalized rings around the McMullen domain ⋮ On hyperbolic rational maps with finitely connected Fatou sets ⋮ Singular perturbations in the quadratic family ⋮ Mandelpinski structures in the parameter planes of rational maps ⋮ SINGULAR PERTURBATIONS OF zⁿ WITH MULTIPLE POLES ⋮ GEOMETRIC LIMITS OF MANDELBROT AND JULIA SETS UNDER DEGREE GROWTH ⋮ On the Hausdorff dimension of the Sierpiński Julia sets ⋮ Julia sets converging to the unit disk ⋮ The McMullen domain: Satellite Mandelbrot sets and Sierpinski holes ⋮ Mandelpinski necklaces in the parameter planes of rational maps ⋮ Singular perturbations of complex polynomials

Cites Work

• Buried Sierpinski curve Julia sets
• Topological characterization of the Sierpiński curve
• The escape trichotomy for singularly perturbed rational maps
• On the dynamics of polynomial-like mappings
• Geometry and Dynamics of Quadratic Rational Maps
• 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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