Campos, BeatrizCanela Sánchez, JordiVindel, Pura2020-05-082020-12-3120181007-5704https://hdl.handle.net/2445/159358In this paper we study the dynamical behavior of the Chebyshev-Halley methods on the family of degree $n$ polynomials $z^{n}+c$. We prove that, despite increasing the degree, it is still possible to draw the parameter space by using the orbit of a single critical point. For the methods having $z=\infty $ as an attracting fixed point, we show how the basins of attraction of the roots become smaller as the value of $n$ grows. We also demonstrate that, although the convergence order of the Chebyshev-Halley family is 3, there is a member of order 4 for each value of $n$. In the case of quadratic polynomials, we bound the set of parameters which correspond to iterative methods with stable behaviour other than the basins of attraction of the roots.18 p.application/pdfengcc-by-nc-nd (c) Elsevier B.V., 2018http://creativecommons.org/licenses/by-nc-nd/3.0/esSistemes de ChebyshevPolinomisChebyshev systemsPolynomialsinfo:eu-repo/semantics/article6734482020-05-08info:eu-repo/semantics/openAccess