  We study generic solutions in a non-minimally coupled to gravity scalar field
cosmology. It is shown that dynamics for both canonical and phantoms scalar
fields with the potential can be reduced to the dynamical system from which the
exact forms for an equation of the state parameter can be derived. We have
found the stationary solutions of the system and discussed their stability.
Within the large class of admissible solutions we have found a non-degenerate
critical points and we pointed out multiple attractor type of trajectory
travelling in neighborhood of three critical points at which we have the
radiation dominating universe, the barotropic matter dominating state and
finally the de Sitter attractor. We have demonstrated the stability of this
trajectory which we call the twister solution. Discovered evolutional path is
only realized if there exist the non-minimal coupling constant. We have found
simple duality relations between twister solutions in phantom and canonical
scalar fields in the radiation domination phase. For the twister trajectory we
have found an oscillating regime of approaching the de Sitter attractor.
