Reconstruction of scalar field and tachyon potentials for closed cosmological models

We develop a technique for the reconstruction of the potential for a scalar field or a tachyon field, reproducing a given cosmological evolution in a closed isotropic cosmological model. Such potentials are explicitly written down for the cases of the evolutions driven by radiation, by a generic barotropic fluid and by radiation plus a cosmological constant, for the case of a scalar field. For tachyon and pseudo-tachyon fields the potentials are reconstructed for the cases of the evolutions driven by the Chaplygin gas, by the anti-Chaplygin gas and for other special cases, corresponding to particular values of the barotropic index.