Business Cycles: Discrete Time

Although we for reasons given prefer to work with continuous time models it must be admitted that there are certain advantages in displaying the details of chaos for discrete time models. This is so because, before the tools of analysis, such as symbolic dynamics, can be applied to the continuous models we need to construct the return map on the Poincaré section for the orbit investigated. This, however, means that we first have to integrate the system over a complete cycle. The details of such an integration can easily become just much too complex.