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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/63103
Newton's method on bring-Jerrard polynomials
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Abstract
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 $c\in\mathbb{R}$
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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CAMPOS, Beatriz, et al. Newton's method on bring-Jerrard polynomials. Publicacions Matemàtiques. 2014. Vol. Extra, num. 81-109. ISSN 0214-1493. [consulted: 10 of June of 2026]. Available at: https://hdl.handle.net/2445/63103