This paper studies the behavior of the moments of a particle distribution as it is transported through a Hamiltonian system. Functions of moments that remain invariant for an arbitrary linear Hamiltonian system are constructed. These functions remain approximately invariant for Hamiltonian systems that are not strongly nonlinear. Consequently, they can be used to characterize the degree of nonlinearity of the system.

• Received 12 July 1991

DOI:https://doi.org/10.1103/PhysRevA.45.2572