II. L. R. Goldberg and J. Milnor

I. Rotation Sets

II. Fixed Point Portraits

II. Douady, Hubbard and Branner have introduced the concept of a "limb" in the Mandelbrot set. A quadratic map f(z)=z^{2}+c belongs to the p/q limb if and only if there exist q external rays of its Julia set which land at a common fixed point of f, and which are permuted by f with combinatorial rotation number p/q in Q/Z, p/q ≠ 0). (Compare Figure 1 and Appendix C, as well as Lemma 2.2.) This note will make a similar analysis of higher degree polynomials by introducing the concept of the "fixed point portrait" of a monic polynomial map.