Stationary Points of Scalar Fields Coupled to Gravity
  We investigate the dynamics of gravity coupled to a scalar field using a non-canonical form of the kinetic term. It is shown that its singular point represents an attractor for classical solutions and the stationary value of the field may occur distant from the minimum of the potential. In this paper properties of universes with such stationary states are considered. We reveal that such state can be responsible for modern dark energy density. 
H. Kroger, G. Melkonyan, F. Paradis, S.G. Rubin