The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems

• Date: 2003
• Main Authors: Prykarpatsky, A. K., Samoilenko, V. G., Taneri, U., Прикарпатський, А. К., Самойленко, В. Г., Танері, У.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2003
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3901
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...