Newton's method on Bring-Jerrard polynomials
In this paper we study the topology of the hyperbolic component of the parameter plane for the Newton's method applied to n-th degree Bring-Jerrard polynomials given by P_n(z) = z^n-cz 1, \ c. For n=5, using the Tschirnhaus-Bring-Jerrard nonlinear transformations, this family controls, at least...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150688 |
| Acesso em linha: | https://ddd.uab.cat/record/150688 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_Extra14_05 |
| Access Level: | acceso abierto |
| Palavra-chave: | Holomorphic dynamics Julia and Fatou sets Hyperbolic components Bifurcation locus Newton's method |
| Resumo: | In this paper we study the topology of the hyperbolic component of the parameter plane for the Newton's method applied to n-th degree Bring-Jerrard polynomials given by P_n(z) = z^n-cz 1, \ c. For n=5, using the Tschirnhaus-Bring-Jerrard nonlinear transformations, this family controls, at least theoretically, the roots of all quintic polynomials. We also study a bifurcation cascade of the bifurcation locus by considering c . |
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