04-2   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Walter Bergweiler:

Quasinormal Families and Periodic Points

Let n >= 2 be an integer and K > 1. By fn we denote the n-th iterate of a function f. Let F be the family of all functions f holomorphic in some domain such that ¦(fn)'(ξ)¦ < = K whenever fn(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 k) of periodic points of period n such that (fn)'(ξk) -> ∞ 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, 55-63

Mail an Jens Burmeister
[Thu Feb 19 18:56:36 2009]