We first introduce the basic concepts of complex dynamics such as Fatou and Julia sets and then discuss for a certain class of entire function, including e.g. functions like sin(az+b), under which conditions the components of the Fatou set are bounded.This is joint work with Lasse Rempe-Gillen and Nuria Fagella.(The link to the relevant paper is  http://arxiv.org/abs/1404.0925 )