2019
Том 71
№ 9

# 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 $G = K \oplus P{\text{, where }}K$ is the Lie algebra of a fixed subgroup $K \subset {\text{G}}$ with respect to an involution σ : GG on the Lie group G, and with a Poisson action of special type on a symplectic matrix manifold.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 2, pp 282-292.

Citation Example: Prykarpatsky A. K., Samoilenko V. G., Taneri U. The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems // Ukr. Mat. Zh. - 2003. - 55, № 2. - pp. 232-240.

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