Articles producció científica> Enginyeria Informàtica i Matemàtiques

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

  • Identification data

    Identifier: imarina:9391713
    Handle: https://hdl.handle.net/20.500.11797/imarina9391713
    Authors:
    Canela, JordiGarijo, AntonioRoesch, Pascale
    Abstract:
    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.

  • Others:

    Author, as appears in the article.: Canela, Jordi; Garijo, Antonio; Roesch, Pascale
    Papper version: info:eu-repo/semantics/submittedVersion
    Department: Enginyeria Informàtica i Matemàtiques
    Funding program: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
    Project code: PID2020-118281GB-C33
    Acronym: ATBiD
    Abstract: 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.
    Journal publication year: 2024
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: antonio.garijo@urv.cat
    Funding program action: Proyectos I+D Generación de Conocimiento
    Publication Type: info:eu-repo/semantics/article

  • Keywords:

    Mathematics,Dynamical Systems

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