Newton's method for symmetric quartic polynomials
Campos, Beatriz (Universitat Jaume I. Departament de Matemàtiques)
Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Vindel, Pura (Universitat Jaume I. Departament de Matemàtiques)

Date:	2016
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.
Grants:	Ministerio de Economía y Competitividad MTM2014-52209-C2-2-P Ministerio de Economía y Competitividad MTM2014-52016-C02-2-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-555
Note:	Agraïments: The third author is partially supported by the Polish NCN grant decision DEC-2012/06/M/ST1/00168. UJI project P1.1B20115-16
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Holomorphic dynamics ; Julia and Fatou sets ; Newton's method
Published in:	Applied Mathematics and Computation, Vol. 290 (2016) , p. 326-335, ISSN 0096-3003

DOI: 10.1016/j.amc.2016.06.021

Postprint 13 p, 906.5 KB

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