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 \(G = K \oplus P{\text{, where }}K\) is the Lie algebra of a fixed subgroup \(K \subset {\text{G}}\) with respect to an...
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| Date: | 2003 |
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| Main Authors: | , , , , , |
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| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3901 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510034173100032 |
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| author | Prykarpatsky, A. K. Samoilenko, V. G. Taneri, U. Прикарпатський, А. К. Самойленко, В. Г. Танері, У. |
| author_facet | Prykarpatsky, A. K. Samoilenko, V. G. Taneri, U. Прикарпатський, А. К. Самойленко, В. Г. Танері, У. |
| author_sort | Prykarpatsky, A. K. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:14:50Z |
| description | 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. |
| first_indexed | 2026-03-24T02:50:34Z |
| format | Article |
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| id | umjimathkievua-article-3901 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:50:34Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e2/19c49ae0d8dbac9e63073e633e3902e2.pdf |
| spelling | umjimathkievua-article-39012020-03-18T20:14:50Z The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems Метод редукцій в теорії Лі-алгебраїчно інтегровних гамільтонових осциляційних систем Prykarpatsky, A. K. Samoilenko, V. G. Taneri, U. Прикарпатський, А. К. Самойленко, В. Г. Танері, У. 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. Вивчаються питампя про повну інтегровність нелінійних осциляційних динамічних систем, що пов'язані, зокрема, як з декомпозицією Картала алгебри Лі $G = K \oplus P$ де $K$ —алгебра Лі деякої (фіксованої) підгрупи $K ⊂ G$ стосовно інволюції $σ : G → G$ в групі Лі $G$, так і з дією Пуассона спеціального вигляду па симплектичпому матричному многовиді. Institute of Mathematics, NAS of Ukraine 2003-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3901 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 2 (2003); 232-240 Український математичний журнал; Том 55 № 2 (2003); 232-240 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/3901/4517 https://umj.imath.kiev.ua/index.php/umj/article/view/3901/4518 Copyright (c) 2003 Prykarpatsky A. K.; Samoilenko V. G.; Taneri U. |
| spellingShingle | Prykarpatsky, A. K. Samoilenko, V. G. Taneri, U. Прикарпатський, А. К. Самойленко, В. Г. Танері, У. The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems |
| title | The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems |
| title_alt | Метод редукцій в теорії Лі-алгебраїчно інтегровних гамільтонових осциляційних систем |
| title_full | The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems |
| title_fullStr | The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems |
| title_full_unstemmed | The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems |
| title_short | The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems |
| title_sort | reduction method in the theory of lie-algebraically integrable oscillatory hamiltonian systems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3901 |
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