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 : G → G on the Lie group G, and with a Poisson action of special type on a symplectic matrix manifold.
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Prykarpats'kyi, A.K., Samoilenko, V.H. & Taneri, U. The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems. Ukrainian Mathematical Journal 55, 282–292 (2003). https://doi.org/10.1023/A:1025416429429
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DOI: https://doi.org/10.1023/A:1025416429429