Dia: Dimecres, 19 de desembre de 2018
Lloc: Aula T1 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Xavier Jarque, Universitat de Barcelona
Títol: The secant map as a plane dynamical system
Resum: We present some results on the dynamical system induced by the secant map on the real plane applied to real polynomials. As it is well known the secant method is a root finding algorithm which does not use the evaluation of the derivative of the corresponding map.
On the one hand we prove that there exist some points, called focal points, belonging to the boundary of the basins of attraction of all fixed points. On the other hand we prove the existence of polynomials for which there are open sets of the plane not convergeging to any of its roots. Finally we will discuss some further dynamical considerations by somehow adding infinity on the field.
Last updated: Sat Dec 15 21:15:41 2018