Newton-like components in the Chebyshev-Halley family of degree \(n\) polynomials

DOI10.1007/S00009-023-02335-ZOpenAlexW4323050551MaRDI QIDQ2687665

Dan Paraschiv

Publication date: 7 March 2023

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.08787

zbMATH Keywords

Newton's methodrational functionsJulia setFatou componentcomplex dynamicsChebyshev-Halley methods

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) Combinatorics and topology in relation with holomorphic dynamical systems (37F20) Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets (37F46)

Cites Work

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• On a family of rational perturbations of the doubling map
• The formula of riemann-hurwitz and iteration of rational functions
• Quasiconformal Surgery in Holomorphic Dynamics
• Dynamics in One Complex Variable. (AM-160)
• How to find all roots of complex polynomials by Newton's method.

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