Dynamics and limiting behavior of Julia sets of König's method for multiple roots

DOI10.1016/j.topol.2017.10.013zbMath1378.65101OpenAlexW2765867784WikidataQ122874659 ScholiaQ122874659MaRDI QIDQ1680126

Gerardo Honorato

Publication date: 22 November 2017

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2017.10.013

zbMATH Keywords

connectednesscomplex dynamicsroot-finding algorithms

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) 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) Numerical computation of roots of polynomial equations (65H04)

Related Items (5)

Regions of convergence and dynamics of Schröder-like iteration formulae as applied to complex polynomial equations with multiple roots ⋮ The link on extraneous non-repelling cycles of Schröder's methods of the first and second kind ⋮ Finite pairs of prescribed cycles of König's and Steffensen's methods for entire functions ⋮ Estimating convergence regions of Schröder's iteration formula: how the Julia set shrinks to the Voronoi boundary ⋮ Disconnected Julia set of Halley's method for exponential maps

Uses Software

• Voronoi

Cites Work

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• On the connectivity of the Julia sets of meromorphic functions
• Polynomial root-finding methods whose basins of attraction approximate Voronoi diagram
• Fatou, Julia, Montel. The Great Prize of mathematical sciences of 1918, and beyond. Transl. from the French
• Optimal control problems for partial differential equations on reticulated domains. Approximation and asymptotic analysis
• Exhibiting chaos and fractals with a microcomputer
• Numerical methods for roots of polynomials. Part I
• Point estimation of root finding methods
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• Newton's method and complex dynamical systems
• Families of rational maps and convergence basins of Newton's method
• Hausdorff convergence of Julia sets
• On extraneous fixed-points of the basic family of iteration functions
• Dynamics of the King and Jarratt iterations
• Numerical methods for roots of polynomials. II
• On local connectivity for the Julia set of rational maps: Newton's famous example
• A class of iterative methods for holomorphic functions
• On Schröder's families of root-finding methods
• On the Julia set of König’s root–finding algorithms
• Complex analytic dynamics on the Riemann sphere
• On the efficiency of algorithms of analysis
• On K nig's root-finding algorithms*
• A small probabilistic universal set of starting points for finding roots of complex polynomials by Newton’s method
• Mean value conjectures for rational maps
• On Newton's method for entire functions
• How to find all roots of complex polynomials by Newton's method.
• Schröder iteration functions associated with a one-parameter family of biquadratic polynomials

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