# On the boundary of the basins of attraction for the secant method

Date:
16.07.19
Times:
11:30 to 12:30
Place:
IMUB-Universitat de Barcelona
Speaker:
Toni Garijo
University:
Universitat Rovira i VIrgili

#### 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 $p$.