1. Julia and Fatou proved this theorem directly from Theorem 11.3.
2. A neutral periodic point is one in which the multiplier is equal to one in modulus. A rationally neutral periodic point is one in which the multiplier is a root of unity, and an irrationally neutral periodic point is one in which the multiplier is one in modulus but is not a root of unity.
3. Singular domains are components of F which converge neither to attracting nor to rationally neutral domains. Sometimes these domains are called rotation domains.
4. It has been shown since that S can be annular and therefore need not contain a fixed point. Iteration then acts like an irrational rotation of an annulus.