Dynamics of composite functions (Q1281655)

Let \(f\) and \(g\) be transcendental entire functions. It is shown that \(f\circ g\) has wandering domains if and only if \(g\circ f\) has wandering domains. The same conclusion holds for the various types of domains arising from the classification of periodic components of the Fatou set. The results have been obtained independently by \textit{W. Bergweiler} and \textit{Y. F. Wang} [Ark. Mat. 36, 31-39 (1998; Zbl 0906.30025)].