# name
Dynamics of the Secant map near infinity

# metadata.dc.description.abstract[].value
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.

# metadata.dc.relation.ispartof[].value
Journal of Difference Equations and Applications, 2022, vol. 28, num. 10, p. 1334-1347

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Dynamics of the Secant map near infinity