# 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 *i* *n*.