  Self-similar, spherically symmetric cosmological models with a perfect fluid
and a scalar field with an exponential potential are investigated. New
variables are defined which lead to a compact state space, and dynamical
systems methods are utilised to analyse the models. Due to the existence of
monotone functions global dynamical results can be deduced. In particular, all
of the future and past attractors for these models are obtained and the global
results are discussed. The essential physical results are that initially
expanding models always evolve away from a massless scalar field model with an
initial singularity and, depending on the parameters of the models, either
recollapse to a second singularity or expand forever towards a flat power-law
inflationary model. The special cases in which there is no barotropic fluid and
in which the scalar field is massless are considered in more detail in order to
illustrate the asymptotic results. Some phase portraits are presented and the
intermediate dynamics and hence the physical properties of the models are
discussed.
