Open Access
2014 Newton's method on Bring-Jerrard polynomials
Beatriz Campos, Antonio Garijo, Xavier Jarque, Pura Vindel
Publ. Mat. 58(S1): 81-109 (2014).


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 $P_n(z) = z^n-cz +1$, $c\in\mathbb{C}$. 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 $c\in \mathbb{R}$.


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Beatriz Campos. Antonio Garijo. Xavier Jarque. Pura Vindel. "Newton's method on Bring-Jerrard polynomials." Publ. Mat. 58 (S1) 81 - 109, 2014.


Published: 2014
First available in Project Euclid: 19 May 2014

zbMATH: 1321.37045
MathSciNet: MR3211828

Primary: 37F10 , 37F45

Keywords: bifurcation locus , holomorphic dynamics , hyperbolic components , Julia and Fatou sets , Newton's method

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.58 • No. S1 • 2014
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