The semigroup approach to the problem of N bodies

The semigroup approach to the problem of N bodies investigation is developed. The differential equation in partial differences for the problems, multitudes problem of N bodies with different initial conditions is shown. On the basis of the physical considerations, invariant transformations for radius-vectors are obtained which with the help of semigroup correlation make the problem of N bodies with special initial conditions possible. The differential equation for 3 bodies problem multitudes with different initial conditions is possible with the help of Ambartsumian's principle of invariance. The possibility of the common solving of this equation is discussed. The examples of the mechanical systems for which we manage to describe further evolution are shown.