Ergodic Theory and Dynamical Systems

Research Article

Iterates of meromorphic functions III: Preperiodic domains

I. N. Bakera1, J. Kotusa2 and Lü Yiniana3

a1 Department of Mathematics, Imperial College, London, SW7 2BZ, UK

a2 Institute of Mathematics, Technical University of Warsaw, 00–661 Warsaw, Poland

a3 Institute of Mathematics, Academia Sinica, Beijing, China

Abstract

The paper discusses the connectivity of periodic and preperiodic domains in the stable set in the iteration of a meromorphic function. The connectivity of an invariant component has one of the values 1, 2, ∞. Examples are constructed to show that the connectivity of a preperiodic component may take any value.

(Received May 25 1990)

(Revised December 01 1990)