In this paper the method of critical curves, a tool for the analysis of the
global dynamical properties of two-dimensional noninvertible maps, is appl
ied 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 t
he role played by absorbing areas, particular trapping regions bounded by p
ortions of critical curves, in the qualitative changes of the attracting se
ts and of the basins of attraction. Such kind of analysis is performed thro
ugh an interplay among analytical, geometrical and numerical techniques.