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http://hdl.handle.net/2445/189352
Title: | Dynamics of the Secant map near infinity |
Author: | Garijo, Antonio Jarque i Ribera, Xavier |
Keywords: | Teoria de la bifurcació Sistemes dinàmics diferenciables Anàlisi numèrica Bifurcation theory Differentiable dynamical systems Numerical analysis |
Issue Date: | 7-Mar-2022 |
Publisher: | Taylor and Francis |
Abstract: | We investigate the root finding algorithm given by the secant method applied to a real polynomial $p$ of degree $k$ as a discrete dynamical system defined on $\mathbb R^2$. We extend the secant map to the real projective plane $\mathbb {R P}^2$. The line at infinity $\ell_{\infty}$ is invariant, and there is one (if $k$ is odd) or two (if $k$ is even) fixed points at $\ell_{\infty}$. We show that these are of saddle type, and this allows us to better understand the dynamics of the secant map near infinity. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1080/10236198.2022.2044476 |
It is part of: | Journal of Difference Equations and Applications, 2022, vol. 28, num. 10, p. 1334-1347 |
URI: | http://hdl.handle.net/2445/189352 |
Related resource: | https://doi.org/10.1080/10236198.2022.2044476 |
ISSN: | 1023-6198 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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725146.pdf | 632.84 kB | Adobe PDF | View/Open |
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