Abstract
We consider classical many-particle systems of identical particles and distinguishable particles. For these types of systems we construct a new representation of a solution to the initial value problem to the BBGKY hierarchy of equations, namely, in the form of an expansion over particle clusters whose evolution is governed by the cumulants (semi-invariants) of the evolution operator of the corresponding particle cluster. Such a representation of solutions enables us to describe the cluster nature of the evolution of infinite particle systems with different symmetry properties in detail. A convergence of the constructed expansions is investigated in the suitable functional spaces.
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