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 $p$, $p'$...
| Authors: | , , , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2016 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/108550 |
| Online Access: | https://hdl.handle.net/2445/108550 |
| Access Level: | Open access |
| Keyword: | Sistemes dinàmics diferenciables Differentiable dynamical systems |
| Summary: | 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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