On the Set of non Normality in Iteration Theory
by
P. Bhattacharyya
Tezpur University, Tezpur - 784028, Assam, India

Let f be a function of the complex variable z. The dynamics of rational and entire trascendental f has been studied extensively since Fatou and Juia introduced the study of iteration of analytic functions in their monumental papers during 1918-20. The set of points of the complex plane where the sequence of iterates of f is not normal (in the sense of Montel)is the Julia set and its complement is the Fatou set. The Julia set is closed and has no interior points unless it is the whole plane. There are examples of functions for which the Julia set is the whole plane. In this paper we prove some theorems giving sufficient conditions for the Julia set of a function will be the whole plane.Apart from the rational and entire transcendental class of functions considered earlier we also consider the class of transcendental meromorphic functions considered by recently by Baker, Kotus and Lu.

Date received: March 1, 2003