Specifying attracting cycles for Newton maps of polynomials

DOI10.1080/10236198.2012.751987zbMath1283.30060arXiv1208.5687OpenAlexW2045554733MaRDI QIDQ2846812

Jared T. Collins, James T. Campbell

Publication date: 3 September 2013

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.5687

zbMATH Keywords

polynomialsNewton methodrational mapsrelaxed Newton methodchaotic complex dynamicsextraneous attractors

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Iteration theory, iterative and composite equations (39B12) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Linear ordinary differential equations and systems in the complex domain (34M03)

Related Items (5)

Constructing attracting cycles for Halley and Schröder maps of polynomials ⋮ Prescribed cycles of König's method for polynomials ⋮ The link on extraneous non-repelling cycles of Schröder's methods of the first and second kind ⋮ Blowup points and baby Mandelbrot sets for a family of singularly perturbed rational maps ⋮ Finite pairs of prescribed cycles of König's and Steffensen's methods for entire functions

Cites Work

• On the iteration of a rational function: Computer experiments with Newton's method
• Holomorphic motions in the parameter space for the relaxed Newton's method
• Attracting cycles for the relaxed Newton's method
• The fundamental theorem of algebra and complexity theory
• The Road to Chaos is Filled with Polynomial Curves

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