Newton's method for symmetric quartic polynomials
We investigate the parameter plane of the Newton's method applied to the family of quartic polynomials $p_{a,b}(z)=z^4+az^3+bz^2+az+1$, where $a$ and $b$ are real parameters. We divide the parameter plane $(a,b) \in \mathbb R^2$ into twelve open and connected {\it regions} where $p$, $p'$...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/108550 |
| Acceso en línea: | https://hdl.handle.net/2445/108550 |
| Access Level: | acceso abierto |
| Palabra clave: | Sistemes dinàmics diferenciables Differentiable dynamical systems |
| Sumario: | We investigate the parameter plane of the Newton's method applied to the family of quartic polynomials $p_{a,b}(z)=z^4+az^3+bz^2+az+1$, where $a$ and $b$ are real parameters. We divide the parameter plane $(a,b) \in \mathbb R^2$ into twelve open and connected {\it regions} where $p$, $p'$ and $p''$ have simple roots. In each of these regions we focus on the study of the Newton's operator acting on the Riemann sphere. |
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