Garijo Real, AntonioJarque i Ribera, Xavier2020-02-172020-10-142019-10-140951-7715https://hdl.handle.net/2445/150446We 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 shape and distribution of the basins of attraction associated to the roots of p , and we also show the existence of other stable dynamics that might affect the efficiency of the algorithm. Finally we extend the secant map to the punctured torus $\mathbb{T}_{\infty}^{2}$ which allow us to better understand the dynamics of the secant method near $\infty$ and facilitate the use of the secant map as a method to find all roots of a polynomial.22 p.application/pdfeng(c) IOP Publishing & London Mathematical Society , 2019Teoria de la bifurcacióFuncions de diverses variables complexesBifurcation theoryFunctions of several complex variablesinfo:eu-repo/semantics/article6959922020-02-17info:eu-repo/semantics/openAccess