Results on escaping set of an entire function and its composition (Q2241666)

Escaping set of entire functions is a very important topics in holomorpic dynamics. A major problem is the ``Eremenko conjecture'' on escaping sets. This paper covers some properties of escaping sets of two permutable transcendental entire functions \(f\circ g=g\circ f\). Among the results discussed in the paper we mention the following ones. The escaping set \(I(f\circ g)\) of \(f\circ g\) is completely invariant under \(f\) and \( g\), and it is a subset of \(I(f)\) and \(I(g)\). If both \(f\) and \(g\) are permutable and of bounded type, so is \(f\circ g\). Moreover, if they are hyperbolic functions of bounded type, then so is \(f\circ g\).