  In the scalar-tensor theory of gravitation it seems nontrivial to establish
if solutions of the cosmological equations in the presence of a cosmological
constant behave as attractors independently of the initial values. We develop a
general formulation in terms of two-dimensional phase space. We show that there
are two kinds of fixed points, one of which is an attractor depending on the
coupling constant and equation of state. In the case with a power-law potential
in the Jordan frame, we also find new type of inflation caused by the coupling
to the matter fluid.
