Newton's method for symmetric quartic polynomials

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Title:	Newton's method for symmetric quartic polynomials
Author:	Campos, Beatriz; Garijo, Antoni; Jarque i Ribera, Xavier; Vindel, Pura
Abstract:	Agraïments: The third author is partially supported by the Polish NCN grant decision DEC-2012/06/M/ST1/00168. UJI project P1.1B20115-16
Abstract:	We investigate the parameter plane of the Newton's method applied to the family of quartic polynomials p_a,b(z)=z^4 az^3 bz^2 az 1, where a and b are real parameters. We divide the parameter plane (a,b) R^2 into twelve open and connected regions where p, p' and p'' have simple roots. In each of these regions we focus on the study of the Newton's operator acting on the Riemann sphere.
Subject(s):	-Holomorphic dynamics -Julia and Fatou sets -Newton's method
Rights:	open access Tots els drets reservats. https://rightsstatements.org/vocab/InC/1.0/
Document type:	Article
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Uri:	https://ddd.uab.cat/record/169488