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2023-03-04

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cc by (c) Dan Paraschiv, 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/217654

Newton-Like Components in the Chebyshev–Halley Family of Degree $n$Polynomials

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https://doi.org/10.1007/s00009-023-02335-z

Abstract

We 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 $f_{n,-1}$.

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Sistemes dinàmics complexos, Funcions holomorfes, Funcions de variables complexes

Subject (English)

Complex dynamical systems, Holomorphic functions, Functions of complex variables

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

PARASCHIV, Dan. Newton-Like Components in the Chebyshev–Halley Family of Degree $n$Polynomials. Mediterranean Journal of Mathematics. 2023. Vol. 20, num. 3. ISSN 1660-5446. [consulted: 10 of August of 2026]. Available at: https://hdl.handle.net/2445/217654

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