  The dynamics of closed scalar field FRW cosmological models is studied for
several types of exponentially and more than exponentially steep potentials.
The parameters of scalar field potentials which allow a chaotic behaviour are
found from numerical investigations. It is argued that analytical studies of
equation of motion at the Euclidean boundary can provide an important
information about the properties of chaotic dynamics. Several types of
transition from chaotic to regular dynamics are described.
