FIXED-POINTS OF POLYNOMIAL MAPS .2. FIXED-POINT PORTRAITS

Douady, Hubbard and Branner have introduced the concept of a ''limb'' in the Mandelbrot set. A quadratic map f(z) = z2 + 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 off, and which are permuted by f with combinatorial rotation number p/q is-an-element-of Q/Z, p/q not-equal 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.