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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:
It is part of: Journal of Difference Equations and Applications, 2022, vol. 28, num. 10, p. 1334-1347
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ISSN: 1023-6198
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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