Abstract
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 $(\mathrm{H\ifmmode \dot{}\else \.{}\fi{}}>0),$ 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.
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