|
Special Issue: Proceedings of RCD Conference 2023
Solvable Algebras and Integrable Systems
Valery V. Kozlovab a Steklov Mathematical Institute of Russian Academy of Science,
ul. Gubkina 8, 119991 Moscow, Russia
b P. G. Demidov Yaroslavl State University,
ul. Sovetskaya 14, 150003 Yaroslavl, Russia
Аннотация:
This paper discusses a range of questions concerning the application of solvable
Lie algebras of vector fields to exact integration of systems of ordinary differential equations.
The set of $n$ independent vector fields generating a solvable Lie algebra in $n$-dimensional space
is locally reduced to some “canonical” form. This reduction is performed constructively (using
quadratures), which, in particular, allows a simultaneous integration of $n$ systems of differential
equations that are generated by these fields. Generalized completely integrable systems are
introduced and their properties are investigated. General ideas are applied to integration of the
Hamiltonian systems of differential equations.
Ключевые слова:
quadratures, solvable alebra, Frobenius theorem, completely integrable systems, Lie
theorem, Hamiltonian systems
Поступила в редакцию: 09.02.2024 Принята в печать: 01.04.2024
Образец цитирования:
Valery V. Kozlov, “Solvable Algebras and Integrable Systems”, Regul. Chaotic Dyn., 29:5 (2024), 717–727
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1277 https://www.mathnet.ru/rus/rcd/v29/i5/p717
|
Статистика просмотров: |
Страница аннотации: | 40 | Список литературы: | 14 |
|