  We derive a new \emph{regular} dynamical system on a 3-dimensional
\emph{compact} state space describing linear scalar perturbations of spatially
flat Robertson-Walker geometries for relativistic models with a minimally
coupled scalar field with an exponential potential. This enables us to
construct the global solution space, illustrated with figures, where known
solutions are shown to reside on special invariant sets. We also use our
dynamical systems approach to obtain new results about the comoving and uniform
density curvature perturbations. Finally we show how to extend our approach to
more general scalar field potentials. This leads to state spaces where the
state space of the models with an exponential potential appears as invariant
boundary sets, thereby illustrating their role as building blocks in a
hierarchy of increasingly complex cosmological models.
