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 behavior
are found from numerical investigations. It is argued that analytical studi
es of equation of motion at the Euclidean boundary can provide an important
information about the properties of chaotic dynamics. Several types of tra
nsition from chaotic to regular dynamics are described.