  Various scenarios of the initial inflation of the universe are distinguished
by the choice of a scalar field {\em potential} $U(\phi)$ which simulates a
{\it temporarily} non--vanishing {\em cosmological term}. Our new method, which
involves a reparametrization in terms of the Hubble expansion parameter $H$,
provides a classification of allowed inflationary potentials and of the
stability of the critical points. It is broad enough to embody all known {\it
exact} solutions involving one scalar field as special cases. Inflation
corresponds to the evolution of critical points of some catastrophe manifold.
The coalescence of its nondegenerate critical points with the creation of a
degenerate critical point corresponds the reheating phase of the universe. This
is illustrated by several examples.
