The inverse limits approach to chaos

When analyzing a dynamic economic model, one fundamental question is are the dynamics simple or chaotic? Inverse limits, as an area of topology, has its origins in the 1920s and since the 1950s has been very useful as a means of constructing “pathological” continua. However, since the 1980s, there is a growing literature linking dynamical systems with inverse limits. In this paper, we review some results from this literature and apply them to the cash-in-advance model of money. In particular, we analyze the inverse limit of the cash-in-advance model of money and illustrate how information about the inverse limit is useful for detecting or ruling out complicated dynamics.