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,...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:313605 |
| Acceso en línea: | https://ddd.uab.cat/record/313605 https://dx.doi.org/urn:doi:10.1137/24M1648090 |
| Access Level: | acceso abierto |
| Palabra clave: | Holomorphic dynamics Singular perturbations Degeneracy parameters Julia sets Root-finding algorithm |
| 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 quasiconformal surgery. |
|---|