The reduction method in the theory of lie-algebraically integrable oscillatory hamiltonian systems

Abstract

We study the problem of the complete integrability of nonlinear oscillatory dynamical systems connected, in particular, both with the Cartan decomposition of a Lie algebra G = K ? P, where K is the Lie algebra of a fixed subgroup K ? G with respect to an involution ?: G ? G on the Lie group G, and with a Poisson action of special type on a symplectic matrix manifold. © 2003 Plenum Publishing Corporation.