03-12   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Walter Bergweiler:

Fixed points of composite meromorphic functions and normal families

We show that there exists a function f meromorphic in the plane C such that the family of all functions g holomorphic in the unit disk D for which f⋅g has no fixed point in D is not normal. This answers a question of Hinchliffe who had shown that this family is normal if \hat{C} \ f(C) does not consist of exactly one point in D. We also investigate the normality of the family of all holomorphic functions g such that f(g(z)) ≠ h(z) for some non-constant meromorphic function h.

Bibliographical note: to appear in Proc. Roy. Soc. Edinburgh Sect. A

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