Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv,

UKRAINE

E-mail: shtyk@imath.kiev.ua

**On the structure of initial value problem of the nonlinear
Bogolyubov hierarchy for classical**
**infinite particle system**

**Abstract:**

We investigate the initial value problem for the sequence of nonlinear
Lioville equations and nonlinear Bogolyubov hierarchy. A solution for the
initial value problem of nonlinear Bogolyubov hierarchy we construct by
way of solutions of the nonlinear Lioville equations and in the form of
the expansion over particle clusters whose evolution is governed by the
certain combination of cumulants of the evolution operator of the corresponding
particle cluster. A convergence of the constructed expansions is investigated
in the space of the sequences of translation-invariant bounded functions.