  Dynamical systems methods are used to investigate dynamics of a flat
Friedmann-Robertson-Walker cosmological model with the non-minimally coupled
scalar field and a potential function. Performed analysis distinguishes the
value of non-minimal coupling constant parameter $\xi=\frac{3}{16}$, which is
the conformal coupling in five dimensional theory of gravity. It is shown that
for a monomial potential functions at infinite values of the scalar field there
exist generic de Sitter and Einstein-de Sitter states. The de Sitter state is
unstable with respect to expansion of the Universe for potential functions
which do not change faster than linearly. This leads to a generic cosmological
evolution without the initial singularity.
