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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2024, том 29, выпуск 5, страницы 717–727 (Mi rcd1277)

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

MSC: 34C14, 37J35

Поступила в редакцию: 09.02.2024
Принята в печать: 01.04.2024

Язык публикации: английский

DOI: 10.1134/S1560354724520022



© МИАН, 2024