The Hamiltonian structure of the BBGKY hierarchy equations

Marsden, J. E., P. J. Morrison and A. Weinstein

Cont. Math. AMS., 28, (1984), 115-124

Abstract:

The BBGKY hierarchy equations for the evolution of the i-point functions of a plasma with electrostatic interactions are shown to be Hamiltonian. The Poisson brackets are Lie-Poisson brackets on the dual of a Lie algebra. This algrebra is constructed from the algebra of n-point functions under Poisson bracket and the filtration obtained by considering subspaces of i-point functions, 1 $\leq$ i $\leq$ n.