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 and the real projective plane  which allow us to better understand the dynamics of the secant method near $infty$.