Dynamics of the Secant map near infinity

Identifier:  imarina:9247853

Handle: https://hdl.handle.net/20.500.11797/imarina9247853

Authors:  Garijo, Antonio; Jarque, Xavier

Abstract:
We investigate the root finding algorithm given by the Secant method applied to a real polynomial p of degree k as a discrete dynamical system defined on R-2. We extend the Secant map to the real projective plane RP2. The line at infinity l(infinity)is invariant, and there is one (if k is odd) or two (if k is even) fixed points at l(infinity ).We show that these are of saddle type, and this allows us to better understand the dynamics of the Secant map near infinity.