HOW IS THE DYNAMICS OF KÖNIG ITERATION FUNCTIONS AFFECTED BY THEIR ADDITIONAL FIXED POINTS?

DOI10.1142/S0218348X99000323zbMath1020.37025MaRDI QIDQ4483533

Vassileios Drakopoulos

Publication date: 12 October 2003

Published in: Fractals (Search for Journal in Brave)

zbMATH Keywords

Julia setsNewton-Raphson methodquadratic polynomialsone-parameter familycubic polynomialsattracting periodic cycleadditional fixed pointshigher-degree rational functionsKönig iteration functions

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 (8)

Are there any Julia sets for the Laguerre iteration function? ⋮ Repellers for the Laguerre Iteration Function ⋮ On optimal fourth-order iterative methods free from second derivative and their dynamics ⋮ The link on extraneous non-repelling cycles of Schröder's methods of the first and second kind ⋮ Symmetries of the Julia sets of König's methods for polynomials ⋮ Local convergence and dynamical analysis of a new family of optimal fourth-order iterative methods ⋮ On the dynamics of a family of third-order iterative functions ⋮ Schröder iteration functions associated with a one-parameter family of biquadratic polynomials

Cites Work

• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• Generalized Computation of Schröder Iteration Functions To Motivate Families of Julia and Mandelbrot-Like Sets
• Chaotic fragmentation in Halley's paradise

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