  The possibility of dynamical stabilization of an internal space is
investigated for a multidimensional cosmological model with minimal coupled
scalar field as inflaton. It is shown that a successful dynamical
compactification crucially depends on the type of interaction between the
geometrical modulus field and the inflaton and its decay products. In the
considered model a stable compactification can be ensured via trapping of the
modulus field by a minimum of the effective potential.
