The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems
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 σ : G → G on the Lie group G, and with a Poisson action of special type on a symplectic matrix manifold., number=2, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Prykarpatsky, A. K. and Samoilenko, V. G. and Taneri, U., year=2003, month=Feb., pages=232–240