Abstract:

We consider the discrete dynamical system $S$ defined on $mathbb R^2$  given by the secant method applied to a real polynomial $p$.  Every simple root $alpha$ of $p$ has associated its basin of attraction $mathcal A(alpha)$  formed by the set of points converging  under $S$ towards $alpha$  and $mathcal A^*(alpha)$ its immediate basin of attraction. We investigate the boundary of the immediate basin of attraction of a root of $p$.