On the dynamics of infinite classical anharmonic systems with constraints

For the infinite systems of classical anharmonic oscillators with constraints, one formulates existence and uniqueness theorems of the solution of the motion equations and of the chain of Bogolyubov equations. One describes the class of constraints (Riemann surfaces that are the configuration spaces of the oscillators) and the class of interactions for which the unique solvability of the motion equations holds under arbitrary initial data.