042  Berichtsreihe des Mathematischen Seminars der Universität Kiel  
Walter Bergweiler:Quasinormal Families and Periodic PointsLet n >= 2 be an integer and K > 1. By f^{n} we denote the nth iterate of a function f. Let F be the family of all functions f holomorphic in some domain such that ¦(f^{n})'(ξ)¦ < = K whenever f^{n}(ξ)=ξ. We show that F is quasinormal of order 1. If K is sufficiently small, then F is normal. We also show that if f is a transcendental entire function, then f has a sequence (ξ_{k}) of periodic points of period n such that (f^{n})'(ξ_{k}) > ∞ as k > ∞. Bibliographical note: in "Complex Analysis and Dynamical Systems II (Nahariya, 2003)," edited by M. Agranovski, L. Karp and D. Shoikhet, Contemp. Math. 382, Amer. Math. Soc., Providence, 2005, 5563

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