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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/189352
Dynamics of the Secant map near infinity
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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.
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GARIJO, Antonio and JARQUE I RIBERA, Xavier. Dynamics of the Secant map near infinity. Journal of Difference Equations and Applications. 2022. Vol. 28, num. 10, pags. 1334-1347. ISSN 1023-6198. [consulted: 17 of June of 2026]. Available at: https://hdl.handle.net/2445/189352