Abstract:

It is known that if we apply Newton's method to the complex function $F(z)=P(z)eQ(z)$, 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. This is a joint work with Figen Cilingir.