Paraschiv, Dan2025-01-202025-01-202023-03-041660-5446https://hdl.handle.net/2445/217654We study the Chebyshev-Halley methods applied to the family of polynomials $f_{n, c}(z)=z^n+c$, for $n \geq 2$ and $c \in \mathbb{C}^*$. We prove the existence of parameters such that the immediate basins of attraction corresponding to the roots of unity are infinitely connected. We also prove that, for $n \geq 2$, the corresponding dynamical plane contains a connected component of the Julia set, which is a quasiconformal deformation of the Julia set of the map obtained by applying Newton's method to $f_{n,-1}$.17 p.application/pdfengcc by (c) Dan Paraschiv, 2023http://creativecommons.org/licenses/by/3.0/es/Sistemes dinàmics complexosFuncions holomorfesFuncions de variables complexesComplex dynamical systemsHolomorphic functionsFunctions of complex variablesinfo:eu-repo/semantics/article2025-01-20info:eu-repo/semantics/openAccess