  In this paper, we prove the existence of super-hyperbolic orbits in four-body
problem, which solves a conjecture of Marchal-Saari. We also prove the
existence of noncollision singularities in the same model, which solves a
conjecture of Anosov. Moreover, the two type of solutions coexist for certain
mass ratios. We also make a conjecture on the classification of final motions
of N-body problem, in which the superhyperbolic type of orbits is one of the
building blocks.
