Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials
Campos, Beatriz (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló)
Canela Sánchez, Jordi (Université Paris-Est Marne-la-Vallée (France))
Vindel, Pura (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló)

Date:	2020
Abstract:	We study the Chebyshev-Halley family of root finding algorithms from the point of view of holomorphic dynamics. Numerical experiments show that the speed of convergence to the roots may be slower when the basins of attraction are not simply connected. In this paper we provide a criterion which guarantees the simple connectivity of the basins of attraction of the roots. We use the criterion for the Chebyshev-Halley methods applied to the degree n polynomials zⁿ +c, obtaining a characterization of the parameters for which all Fatou components are simply connected and, therefore, the Julia set is connected. We also study how increasing n affects the dynamics.
Grants:	Ministerio de Economía y Competitividad MTM2014-52016-C02-2-P
Note:	Altres ajuts: Generalitat Valenciana Project PROMETEO/2016/089 and UJI project P1.1B2015-16
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Iterative methods ; Complex dynamics of rational functions ; Chebyshev-Halley family ; Parameter plane
Published in:	Communications in nonlinear science and numerical simulation, Vol. 82 (March 2020) , art. 105026, ISSN 1007-5704

DOI: 10.1016/j.cnsns.2019.105026

Postprint 27 p, 6.8 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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