Reconstruction of scalar potentials in two-field cosmological models

We study the procedure of the reconstruction of phantom-scalar field potentials in two-field cosmological models. It is shown that, while in the one-field case the chosen cosmological evolution defines uniquely the form of the scalar potential, in the two-field case one has an infinite number of possibilities. The classification of a large class of possible potentials is presented and the dependence of cosmological dynamics on the choice of initial conditions is investigated qualitatively and numerically for two particular models.