  The dynamics of a universe dominated by a self-interacting nonminimally
coupled scalar field are considered. The structure of the phase space and
complete phase portraits are given. New dynamical behaviors include
superinflation ($\dot{H}>0$), avoidance of big bang singularities through
classical birth of the universe, and spontaneous entry into and exit from
inflation. This model is promising for describing quintessence as a
nonminimally coupled scalar field.
