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Dynamics in One Complex Variable. (AM-160), 3rd Edition by John Milnor

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§18. Polynomial Dynamics: External Rays

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

images

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 rf so that every point z in the neighborhood |z| > rf 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 ...

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