Asset price dynamics in a financial market with fundamentalists and chartists

In this paper we consider a model of the dynamics of speculative markets in volving the interaction of fundamentalists and chartists. The dynamics of t he model are driven by a two-dimensional map that in the space of the param eters displays regions of invertibility and noninvertibility. The paper foc uses on a study of local and global bifurcations which drastically change t he qualitative structure of the basins of attraction of several, often coex istent, attracting sets. We make use of the theory of critical curves assoc iated with noninvertible maps, as well as of homoclinic bifurcations and ho moclinic orbits of saddles in regimes of invertibility.