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-degree Bring<br>Jerrard polynomials given by $P_{n}(z)=z^{n}-cz +1, c \in \mathbb{C}$. For $n=5$ using the Tschirnhaus<br>Bring<br>Jerrard nonlinear tran...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/63103 |
| Acesso em linha: | https://hdl.handle.net/2445/63103 |
| Access Level: | acceso abierto |
| Palavra-chave: | Sistemes dinàmics diferenciables Dinàmica topològica Differentiable dynamical systems Topological dynamics |
| Resumo: | In this paper we study the topology of the hyperbolic component of the parameter plane for the Newton's method applied to n-degree Bring<br>Jerrard polynomials given by $P_{n}(z)=z^{n}-cz +1, c \in \mathbb{C}$. For $n=5$ using the Tschirnhaus<br>Bring<br>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 $c\in\mathbb{R}$ |
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