Viacheslav SHTYK
Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv,

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

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.