Connected McMullen-like Julia sets in a Chebyshev-Halley family

In this paper we study a one parameter family of rational maps obtained by applying the Chebyshev-Halley root finding algorithms. We show that the dynamics near parameters where the family presents some degeneracy might be understood from the point of view of singular perturbations. More precisely,...

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Detalles Bibliográficos
Autor: Canela, Jordi; Garijo, Antonio; Roesch, Pascale
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2024
País:España
Institución:Universitat Rovira i virgili (URV)
Repositorio:Repositori Institucional de la Universitat Rovira i Virgili
OAI Identifier:oai:urv.cat:imarina:9391713
Acceso en línea:https://hdl.handle.net/20.500.11797/imarina9391713
Access Level:acceso abierto
Palabra clave:Mathematics,Dynamical Systems
Descripción
Sumario:In this paper we study a one parameter family of rational maps obtained by applying the Chebyshev-Halley root finding algorithms. We show that the dynamics near parameters where the family presents some degeneracy might be understood from the point of view of singular perturbations. More precisely, we relate the dynamics of those maps with the one of the McMullen family Mλ(z)=z4+λ/z2, using quasi-conformal surgery.