This work attempts to utilise perturbation theory to derive discrete mappings which describe the dynamical behaviour of a continuous, and a discrete, chaotic system. The first three chapters introduce some background to the theory of chaotic behaviour In discrete and continuous systems. Chapter 4 considers the dynamical behaviour of Duffings equation. Perturbation theory is applied to Hamiltonian solutions of the system, and a 1-D mapping is derived which models the bifurcation of the system to chaos. Chapter 5 introduces a 2-D chaotic difference map. The qualitative dynamics of the system are investigated and a form of perturbation theory is applied to a parameterised version of the map. The perturbative solutions are shown to exhibit dynamical behaviour very like the original system.