Immediate and virtual basins of Newton's method for entire functions.

DOI10.5802/aif.2184zbMath1103.30015arXivmath/0403336OpenAlexW1490101027MaRDI QIDQ2488753

Sebastian Mayer, Dierk Schleicher

Publication date: 15 May 2006

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0403336

zbMATH Keywords

entire functionNewton methodimmediate basinvirtual basin

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) Dynamical systems in numerical analysis (37N30)

Related Items (16)

Derivative free iterative methods for nonlinear systems ⋮ Moduli space of cubic Newton maps ⋮ Absorbing sets and Baker domains for holomorphic maps ⋮ An optimal fourth-order family of modified Cauchy methods for finding solutions of nonlinear equations and their dynamical behavior ⋮ The Riemann Hypothesis and Holomorphic Index in Complex Dynamics ⋮ Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems ⋮ On the connectivity of the Julia sets of meromorphic functions ⋮ Newton maps of complex exponential functions and parabolic surgery ⋮ Stable high-order iterative methods for solving nonlinear models ⋮ Dynamics of functions arising from Pisot and Salem polynomials ⋮ Newton's method and Baker domains ⋮ Local Convergence of a Family of Iterative Methods with Sixth and Seventh Order Convergence Under Weak Conditions ⋮ A characterization of postcritically minimal Newton maps of complex exponential functions ⋮ On the Julia set of König’s root–finding algorithms ⋮ Accesses to infinity from Fatou components ⋮ On the efficient global dynamics of Newton’s method for complex polynomials

Cites Work

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• Dynamic rays of bounded-type entire functions
• On infinite area for complex exponential function
• On the number of iterations of Newton's method for complex polynomials
• On the efficiency of algorithms of analysis
• Iteration and the Solution of Functional Equations for Functions Analytic In the Unit Disk
• Newton’s method on the complex exponential function
• Iteration of meromorphic functions
• Weakly repelling fixpoints and the connectivity of wandering domains
• Virtual immediate basins of Newton maps and asymptotic values
• How to find all roots of complex polynomials by Newton's method.

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