Let G is contained in C be a domain in the complex plane, and let f: G → G be an analytic function mapping G into itself. By f~n we denote the nth iterate f~n = f o • • • o f (n times) of f. The behavior of the sequence (f~n)_n as n → ∞ is of great interest and has already been studied in depth for the most important choices of G. If G = C, then f is a rational function. Many significant results have been proved during the last years (see e.g. [B2; CG; Mi; S]). In the case G = C, the function f is an entire function; see [Be] for an excellent overview. If G is the unit disk, G = D, then the situation becomes easier, since in this case the family { f~n | n ∈ N} is normal. Initial results have been discovered by Julia, Wolff, and Valiron (see e.g. [V]); further results have been found by Pommerenke and Baker [P; BaP] and by Cowen [C].
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