The Julia sets of Chebyshev's method with small degrees

DOI10.1007/s11071-022-07648-4zbMath1519.37042arXiv2201.11055OpenAlexW4285394513WikidataQ121073098 ScholiaQ121073098MaRDI QIDQ6094448

Tarakanta Nayak, Soumen Pal

Publication date: 13 September 2023

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.11055

zbMATH Keywords

extraneous fixed pointsChebyshev's methodconnected Julia sets

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Cites Work

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• Connectivity of the Julia set for the Chebyshev-Halley family on degree \(n\) polynomials
• Additive perturbed generalized Mandelbrot-Julia sets
• Research on fractal structure of generalized M--J sets utilized Lyapunov exponents and periodic scanning techniques
• On the Julia set of König’s root–finding algorithms
• On K nig's root-finding algorithms*
• Julia sets for the super-Newton method, Cauchy’s method, and Halley’s method
• Dynamics in One Complex Variable. (AM-160)
• How to find all roots of complex polynomials by Newton's method.

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