A new generic and structurally stable cosmological model without
  singularity
  Dynamical systems methods are used to investigate a cosmological model with
non-minimally coupled scalar field and asymptotically quadratic potential
function. We found that for values of the non-minimal coupling constant
parameter $\frac{3}{16}<\xi<\frac{1}{4}$ there exists an unstable asymptotic de
Sitter state, free from a parallelly propagated singularity for
$\frac{5}{24}\le\xi<\frac{1}{4}$, giving rise to non-singular beginning of the
universe. The energy density associated with this state depends on value of the
non-minimal coupling constant and can be much smaller than the Planck energy
density. For $\xi=\frac{1}{4}$ we found that the initial state is in form of
the static Einstein universe. Proposed evolutional model, contrary to the
seminal Starobinsky's model, do not depend on the specific choice of initial
conditions in phase space, moreover, a small change in the model parameters do
not change the evolution thus the model is generic and structurally stable. The
values of the non-minimal coupling constant can indicate for a new fundamental
symmetry in the gravitational theory. We show that Jordan frame and Einstein
frame formulation of the theory are physically nonequivalent.
