Symmetries of the Julia sets of Newton's method for multiple root

DOI10.1016/J.AMC.2010.07.061zbMath1207.65049OpenAlexW1999552491WikidataQ122947741 ScholiaQ122947741MaRDI QIDQ606805

Weifeng Yang

Publication date: 18 November 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.07.061

zbMATH Keywords

Newton's methodJulia setpolynomialmultiple rootsgroup of symmetriesconformal Euclidean isometry

Mathematics Subject Classification ID

Numerical computation of roots of polynomial equations (65H04)

Related Items (8)

New multi-scroll attractors obtained via Julia set mapping ⋮ On the spatial Julia set generated by fractional Lotka-Volterra system with noise ⋮ Influence of the multiplicity of the roots on the basins of attraction of Newton's method ⋮ Real dynamics for damped Newton's method applied to cubic polynomials ⋮ Symmetries of the Julia sets of König's methods for polynomials ⋮ Bivariate Newton-Raphson method and toroidal attraction basins ⋮ Conjugacies of the Newton maps of rational functions ⋮ Reducing chaos and bifurcations in Newton-type methods

Cites Work

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• Complex dynamics
• The Julia set of Newton's method for multiple root
• Julia sets for the standard Newton's method, Halley's method, and Schröder's method
• Symmetries of Julia Sets
• JULIA SETS OF GENERALIZED NEWTON'S METHOD
• JULIA SET OF THE NEWTON TRANSFORMATION FOR SOLVING SOME COMPLEX EXPONENTIAL EQUATION
• A problem of Julia sets
• The components of a Julia set
• Translation invariant Julia sets

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