Newton's method for symmetric quartic polynomials

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 ro...

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Detalles Bibliográficos
Autores: Campos, Beatriz|||0000-0001-9205-0256, Garijo, Antoni|||0000-0002-1503-7514, Jarque i Ribera, Xavier|||0000-0002-6576-9780, Vindel, Pura|||0000-0001-8422-4738
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169488
Acceso en línea:https://ddd.uab.cat/record/169488
https://dx.doi.org/urn:doi:10.1016/j.amc.2016.06.021
Access Level:acceso abierto
Palabra clave:Holomorphic dynamics
Julia and Fatou sets
Newton's method
Descripción
Sumario: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.