  The grazing bifurcation is considered for the Newtonian model of vibro-impact
systems. A brief review on the conditions, sufficient for existence of a
grazing family of periodic solutions, is given. The properties of these
periodic solutions are discussed. A plenty of results on the topological
structure of attractors of vibro-impact systems is known. However, since the
considered system is strongly nonlinear, these attractors may be invisible or,
at least, very sensitive to changes of parameters of the system. On the other
hand, they are observed in experiments and numerical simulations. We offer
(Theorem 2) an approach which allows to explain this contradiction and give a
new robust mathematical model of the non-hyperbolic dynamics in the
neighborhood of grazing.
