On the dynamics of composition of entire functions
by
Anand Prakash Singh
Department of Mathematics, University of Jammu, Jammu-180006, India

Let f be an entire function. For n in N, let fⁿ denote the n-th iterate of f. The set

F(f) = {z : (fn) is normal in some neighbourhood of z }

is the Fatou set or the set of normality and its complement J(f) is the Julia set. If U is a component of F(f), then f(U) lies in some component V of F(f). If U_n \cap U_m = \phi for n =/= m where U_n denotes the component of F(f) which contains fⁿ(U), then U is called a wandering domain, else U is called a pre-periodic domain, and if U_n = U for some n in N then U is called periodic domain.

It is known that for entire functions f and g, f(g) has wandering domain if and only if g(f) has wandering domain. In this paper we discuss the existence of wandering domains of composite entire functions with regards to its factors f and g.

Date received: April 22, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahk-06.