Critical curves and bifurcations of absorbing areas in a financial model

In this paper the method of critical curves, a tool for the analysis of the global dynamical properties of two-dimensional noninvertible maps, is applied to study the dynamics of speculative markets, based on the interaction of different types of traders. The main purpose of the paper is to stress the role played by absorbing areas, particular trapping regions bounded by portions of critical curves, in the qualitative changes of the attracting sets and of the basins of attraction. Such kind of analysis is performed through an interplay among analytical, geometrical and numerical techniques.