  Theory of gravity with a quadratic contribution of scalar curvature is
investigated in terms of dynamical system approach. The simplest
Friedmann-Robertson-Walker metric is used to formulate dynamics in Jordan frame
as well as in conformally transformed Einstein frame. We show that in both
frames there are stable de Sitter states for which the Hubble function
expansion naturally gives terms corresponding to non-substantial dark matter.
Using invariant centre manifold we show that in the Einstein frame there is a
zero measure set of initial conditions leading from unstable to stable de
Sitter state. Additionally, the initial de Sitter state is plunged with a
parallelly propagated singularity. We show that the Jordan frame and the
Einstein frame formulation of the theory are physically nonequivalent.
