Chaos in closed isotropic cosmological models with steep scalar field potential

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 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.