Abstract

We investigate the root finding algorithm given by the secant method applied to a real polynomial $p$ as a discrete dynamical system defined on $mathbb R^2$. We study the main dynamical properties associated to the basins of attraction of the roots of $p$ and show the existence of stable dynamics not related to them. We extend the secant map to the punctured torus  $mathbb T^2_{infty}$ and the real projective plane $mathbb {R P}^2$ which allow us to better understand the dynamics of the secant method near $infty$.