Work

Connected McMullen-Like Julia Sets in a Chebyshev–Halley Family

Year: 2025

Type: article

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 [Formula: see text], using quasiconformal surgery.

Source: SIAM Journal on Applied Dynamical Systems

DOI: 10.1137/24m1648090

Authors: Jordi Canela, Antonio Garijo, Pascale Roesch

Institutions: Universitat Jaume I, Universitat Rovira i Virgili, Université Toulouse III - Paul Sabatier, Institut de Mathématiques de Toulouse

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Generalitat de Catalunya

Awards: G5005173022, Centre International de Mathématiques et d'Informatique (de Toulouse)