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

CHAOS IN CLOSED ISOTROPIC COSMOLOGICAL MODELS WITH STEEP SCALAR FIELD POTENTIAL