Singular perturbations of complex polynomials

DOI10.1090/S0273-0979-2013-01410-1zbMath1277.37074OpenAlexW2022888254MaRDI QIDQ2849008

Robert L. Devaney

Publication date: 16 September 2013

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

Full work available at URL: https://doi.org/10.1090/s0273-0979-2013-01410-1

zbMATH Keywords

polynomial dynamicsperturbationsJulia settopological structureCantor sets of circlesCantor websMandelpinski necklacessingularly perturbed complex polynomials

Mathematics Subject Classification ID

Related Items (22)

RINGS AROUND SIERPINSKI HOLES ⋮ Accessible Mandelbrot sets in the family \(z^n + \lambda /z^n\) ⋮ Singular perturbations with multiple poles of the simple polynomials ⋮ A Mandelpinski maze for rational maps of the form \(z^n + \lambda / z^d\) ⋮ Exotic topology in complex dynamics ⋮ On McMullen-like mappings ⋮ Escape components of McMullen maps ⋮ Generalized rings around the McMullen domain ⋮ Singular perturbations of the unicritical polynomials with two parameters ⋮ Blowup points and baby Mandelbrot sets for a family of singularly perturbed rational maps ⋮ Mandelpinski structures in the parameter planes of rational maps ⋮ Dipoles and pixie dust ⋮ On the dynamics of n-circle inversion ⋮ On the dynamics of a family of singularly perturbed rational maps ⋮ Invariant Jordan curves of Sierpiński carpet rational maps ⋮ Quasisymmetric geometry of the Julia sets of McMullen maps ⋮ On the Hausdorff dimension of the Sierpiński Julia sets ⋮ Dynamics, topology and bifurcations of McMullen maps ⋮ Mandelpinski spokes in the parameter planes of rational maps ⋮ Parameter Planes for Complex Analytic Maps ⋮ Interactions of the Julia Set with Critical and (Un)Stable Sets in an Angle-Doubling Map on ℂ\{0} ⋮ Asymptotics of the Hausdorff dimensions of the Julia sets of McMullen maps with error bounds*

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