  We consider the dynamics of a spatially flat universe dominated by a
self-interacting nonminimally coupled scalar field. The structure of the phase
space and complete phase portraits for the conformal coupling case are given.
It is shown that the non-minimal coupling modifies drastically the dynamics of
the universe. New cosmological behaviors are identified, including
superinflation ($\dot{H}>0$), avoidance of big bang singularities through
classical birth of the universe from empty Minkowski space, and spontaneous
entry into and exit from inflation. The relevance of this model to the
description of quintessence is discussed.
