Newton’s method on Bring-Jerrard polynomials

• Autores: Beatriz Campos Sancho , Antonio Garijo Real , Xavier Jarque Ribera , María Purificación Vindel Cañas
• Localización: Publicacions matematiques, ISSN 0214-1493, Nº. Extra 0 (Proceedings of the Conference “New Trends in Dynamical Systems” held in Salou (Tarragona), Spain, 1-), 2014, págs. 81-109
• Idioma: inglés
• DOI: 10.5565/PUBLMAT_Extra14_05
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    The first and fourth authors were partially supported by P11B2011-30 (Universitat Jaume I) and by the Spanish grant MTM2011-28636-C02-02. The second and third authors were partially supported by the Catalan grant 2009SGR-792, and by the Spanish grant MTM2011-26995-C02-02. The third author also wants to thank the support of the Polish NCN grant decision DEC-2012/06/M/ST1/00168.

  • English

    In this paper we study the topology of the hyperbolic component of the parameter plane for the Newton’s method applied to n-degree Bring–Jerrard polynomials given by Pn(z) = z n − cz + 1, c ∈ C. For n = 5, using the Tschirnhaus– Bring–Jerrard nonlinear transformations, this family controls, at least theoretically, the roots of all quintic polynomials. We also study a bifurcation cascade of the bifurcation locus by considering c ∈ R.