Extrinsic Information Transfer (or EXIT) charts have provided a useful tool for analysing the convergence of iterative decoders. In this work, we abstract the EXIT chart as a feedback interconnection of two one-dimensional dynamical systems. For such feedback interconnections, we characterise the local stability properties of fixed points and demonstrate the existence of period two orbits and discuss their stability properties. Finally, we give a graphical procedure for finding the region of attraction for asymptotically stable fixed points or period two orbits.