Towards generic cosmological evolution without singularity and
  fundamental symmetry of space-time
  Dynamical systems methods are used to investigate cosmological model with
non-minimally coupled scalar field. Existence of an asymptotically unstable de
Sitter state distinguishes values of the non-minimal coupling constant
parameter $\frac{3}{16}\le\xi<\frac{1}{4}$, which correspond to conformal
coupling in higher dimensional theories of gravity.
