Coexisting attractors and complex basins in discrete-time economic models

In this chapter, we consider discrete time dynamical systems with coexistingattractors, and we analyze the problem of the structure of the boundaries that separate their basins of attraction. This problem may become particularly challengingwhen the discrete dynamical system is represented by the iteration of a noninvertiblemap, because in this case nonconnected basins can be obtained, formed by several(even infinitely many) disjoint portions. Measure theoretic attractors, known asMilnor attractors, are also described, together with riddled basins, an extreme formof complex basin’s structure that can be observed in the presence of such attractors.Some tools for the study of global bifurcations that lead to the creation of complexstructures of the basins are described, as well as some applications in discrete timemodels taken from economic dynamics.