  We investigate dynamics of a flat FRW cosmological model with a barotropic
matter and a non-minimally coupled scalar field (both canonical and phantom).
In our approach we do not assume any specific form of a potential function for
the scalar field and we are looking for generic scenarios of evolution. We show
that dynamics of universe can be reduced to a 3-dimensional dynamical system.
We have found the set of fixed points and established their character. These
critical points represent all important epochs in evolution of the universe :
(a) a finite scale factor singularity, (b) an inflation (rapid-roll and
slow-roll), (c) a radiation domination, (d) a matter domination and (e) a
quintessence era. We have shown that the inflation, the radiation and matter
domination epochs are transient ones and last for a finite amount of time. The
existence of the radiation domination epoch is purely the effect of a
non-minimal coupling constant. We show the existence of a twister type solution
wandering between all these critical points.
