Cosmological dynamics with non-minimally coupled scalar field and a
  constant potential function
  Dynamical systems methods are used to investigate global behavior of the
spatially flat Friedmann-Robertson-Walker cosmological model in gravitational
theory with a non-minimally coupled scalar field and a constant potential
function. We show that the system can be reduced to an autonomous
three-dimensional dynamical system and additionally is equipped with an
invariant manifold corresponding to an accelerated expansion of the universe.
Using this invariant manifold we find an exact solution of the reduced
dynamics. We investigate all solutions for all admissible initial conditions
using theory of dynamical systems to obtain a classification of all evolutional
paths. The right-hand sides of the dynamical system depend crucially on the
value of the non-minimal coupling constant therefore we study bifurcation
values of this parameter under which the structure of the phase space changes
qualitatively. We found a special bifurcation value of the non-minimal coupling
constant which is distinguished by dynamics of the model and may suggest some
additional symmetry in matter sector of the theory.
