  Local and global phase-space descriptions and averaging methods are used to
find qualitative features of solutions for the FLRW and the Bianchi I metrics
in the context of scalar field cosmologies with arbitrary potentials and
arbitrary couplings to matter. The stability of the equilibrium points in a
phase-space as well as the dynamics in the regime where the scalar field
diverges are studied. Equilibrium points that represent some solutions of
cosmological interest such as: several types of scaling solutions, a kinetic
dominated solution representing a stiff fluid, a solution dominated by an
effective energy density of geometric origin, a quintessence scalar field
dominated solution, the vacuum de Sitter solution associated to the minimum of
the potential, and a non-interacting matter dominated solution are obtained.
All reveal a very rich cosmological phenomenology.
