A topological analysis of a family of dynamical systems with non-standard chaotic and periodic behaviour

We examine a family of maps, which are motivated by a specific flow model for a manufacturing system, that act on polygons inscribed within an equilateral triangle. The family of maps is interesting because it provides an example of chaotic behaviour in one extreme and periodic behaviour in the other, with a non-standard transition between these extremes. We characterize the behaviour of this family of maps and describe the interesting phenomena which occur between the two extremes of chaos and periodicity. We also use symbolic dynamics to relate one of the maps to a particular subshift of finite type.