Newton's method on bring-Jerrard polynomials

In this paper we study the topology of the hyperbolic component of the parameter plane for the Newton's method applied to n-degree BringJerrard polynomials given by $P_{n}(z)=z^{n}-cz +1, c \in \mathbb{C}$. For $n=5$ using the TschirnhausBringJerrard 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}