Abstract

We consider the secant method applied to a polynomial $p$  as a dynamical system acting on the real plane. If the polynomial $p$ has a local extrema at $alpha$ then the Secant map exhibits a 3-cycle at the point $(alpha,alpha)$. We propose a model map $T$ to explain the behavior of $S^3$ near the point $(alpha,alpha)$. This is a joint work with Ernest Fontich and Xavier Jarque.