  We analyze solutions to Friedmann-Robertson-Walker cosmologies in Brans-Dicke
theory, where a scalar field is coupled to gravity. Matter is modelled by a
$\gamma$-law perfect fluid, including false-vacuum energy as a special case.
Through a change of variables, we reduce the field equations from fourth order
to second order, and they become equivalent to a two-dimensional dynamical
system. We then analyze the entire solution space of this dynamical system, and
find that many qualitative features of these cosmologies can be gleaned,
including standard non-inflationary or extended inflationary expansion, but
also including bifurcations of stable or unstable expansion or contraction,
noninflationary vacuum-energy dominated models, and several varieties of
``coasting," ``bouncing," ``hesitating," and ``vacillating" universes. It is
shown that inflationary dogma, which states that a universe with curvature and
dominated by inflationary matter will always approach a corresponding
flat-space solution at late times, does not hold in general for the
scalar-tensor theory, but rather that the occurence of inflation depends upon
the initial energy of the scalar field relative to the expansion rate. In the
case of flat space ($k=0$), the dynamical system formalism generates some
previously known exact power-law solutions.
