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 ${\mathrm{V(\phi )=\Lambda e}}^{\mathrm{k\phi }}$ . 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.