### §18. Polynomial Dynamics: External Rays

First recall some definitions from §9. Let be a monic polynomial map

with *n* ≥ 2. (In this section, the degree will be denoted by *n*.) Then *f* has a superattracting fixed point at infinity. In particular, it is not difficult to find a constant *r*_{f} so that every point *z* in the neighborhood |*z*| > *r*_{f} of infinity belongs to the basin of attraction *A*(∞). The complement of the basin *A*(∞), that is, the set of all points *z* ∈ with bounded forward orbit under *f*, is called the *filled Julia set* *K* = *K*(*f*). By Lemma 9.4, this ...