JULIA SETS OF GENERALIZED NEWTON'S METHOD

DOI10.1142/S0218348X07003733zbMath1142.37036WikidataQ123345331 ScholiaQ123345331MaRDI QIDQ3510245

Xing-Yuan Wang, Ting-Ting Wang

Publication date: 2 July 2008

Published in: Fractals (Search for Journal in Brave)

zbMATH Keywords

fixed pointsiteration methodbasins of attractionJulia sets theory

Mathematics Subject Classification ID

Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Numerical computation of solutions to single equations (65H05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (4)

Symmetries of the Julia sets of Newton's method for multiple root ⋮ Influence of the multiplicity of the roots on the basins of attraction of Newton's method ⋮ Julia sets of Newton's method for a class of complex-exponential function \(F(z)=P(z)e^{Q(z)}\) ⋮ Bivariate Newton-Raphson method and toroidal attraction basins

Cites Work

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• On the iteration of a rational function: Computer experiments with Newton's method
• Cayley's problem and Julia sets
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• Newton's method and complex dynamical systems
• The complex dynamics of Newton's method for a double root
• The Newton and Halley Methods for Complex Roots
• Surgery for relaxed newton's method
• GENERALIZATIONS OF NEWTON'S METHOD

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