  Using the dynamical system approach, we describe the general dynamics of
cosmological scalar fields in terms of critical points and heteroclinic lines.
It is found that critical points describe the initial and final states of the
scalar field dynamics, but that heteroclinic lines which give a more complete
description of the evolution in between the critical points. In particular, the
heteroclinic line that departs from the (saddle) critical point of perfect
fluid-domination is the representative path in phase space of quintessence
fields that may be viable dark energy candidates. We also discuss the attractor
properties of the heteroclinic lines, and their importance for the description
of thawing and freezing fields.
