Abstract:
The hierarchy of Bogolyubov type (BBGKY) kinetic equations for infinite
classical and quantum lattice systems is considered. A formula for solving
the Cauchy problem for the equations in the form $F(t)=PS(-t)F^0$ is obtained;
here, $P$ is the operator of projection onto the subspace of sequences of
finitely additive measures satisfying consistency conditions. Proofs are
given of the uniqueness of the solution and the group property of the evolution
operator in the situation when the observables are specified by uniformly
continuous functions. Stationary solutions of the equations are obtained.
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