On Newton's method applied to real polynomials

Agraïments: The first author would also like to thank the Ministerio de Ciencia y Innovacion of Spain for the financial support when visiting Boston University.It is known that if we apply Newton's method to the complex function F(z) = P(z)e Q(z), with deg(Q) > 2, then the immediate basin of attraction of the roots of P has finite area. In this paper we show that under certain conditions on P, if deg(Q) = 1, then there is at least one immediate basin of attraction having infinite area

On Newton's method applied to real polynomials

Agraïments: The first author would also like to thank the Ministerio de Ciencia y Innovacion of Spain for the financial support when visiting Boston University.It is known that if we apply Newton's method to the complex function F(z) = P(z)e Q(z), with deg(Q) > 2, then the immediate basin of attraction of the roots of P has finite area. In this paper we show that under certain conditions on P, if deg(Q) = 1, then there is at least one immediate basin of attraction having infinite area