Homogeneous scalar field cosmologies with an exponential potential

We shall study spatially homogeneous cosmological models containing a self-interacting scalar field with an exponential potential of the form V(phi) = Lambda e(k phi). The asymptotic properties of these models are discussed. In particular, their possible isotropization and inflation are investigated for all values of the parameter k. A particular class of models is analyzed qualitatively using the theory of dynamical systems, illustrating the general asymptotic behavior. (C) 1997 American Institute of Physics.