Resumen de Newton’s method on Bring-Jerrard polynomials

Beatriz Campos Sancho, Antonio Garijo Real, Xavier Jarque Ribera, María Purificación Vindel Cañas

• English

  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.