可解代数和积分系统

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2024-05-06 DOI:10.1134/S1560354724520022

Valery V. Kozlov

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引用次数: 0

摘要

本文讨论了有关可解向量场的李代数在常微分方程系统的精确积分中的应用的一系列问题。在 \(n\) 维空间中生成可解李代数的 \(n\) 独立向量场集被局部还原为某种 "典型 "形式。引入了广义完全可积分系统，并研究了它们的性质。

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Solvable Algebras and Integrable Systems

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.

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.