1 Some Methods for the Global Analysis of Closed Invariant Curves in Two-Dimensional Maps

It is well known that models of nonlinear oscillators applied to the study of the business cycle can be formulated both as continuos or discrete time dynamic models (see e.g. [23], [33], [34]). However, economic time is often discontinuous (discrete) because decisions in economics cannot be continuously revised. For this reason discrete-time dynamical systems, represented by difference equations or, more properly, by the iterated application of maps, are often a more suitable tool for modelling dynamic economic processes. So, it is useful to study the peculiarities of discrete dynamical systems and their possible applications to the study of self sustained oscillations. This is the main goal of this Chapter, where we describe, on the light of some recent results about local and global properties of iterated maps of the plane, some particular routes to the creation/destruction of closed invariant curves, along which self sustained oscillations occur.