旋转和可积性

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2024-12-03 DOI:10.1134/S1560354724060029

Andrey V. Tsiganov

引用次数: 0

摘要

讨论了\(n\)维欧氏空间中在\(m\geqslant n-2\)旋转下不变的可积和超可积系统族。不变哈密顿量\(H=\sum p_{i}^{2}+V(q)\)与运动\(M_{\alpha}\)的\(n-2\)积分和运动\(G\)的附加积分可积，它们分别是动量的一阶和四阶多项式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Rotations and Integrability

We discuss some families of integrable and superintegrable systems in \(n\)-dimensional Euclidean space which are invariant under \(m\geqslant n-2\) rotations. The invariant Hamiltonian \(H=\sum p_{i}^{2}+V(q)\) is integrable with \(n-2\) integrals of motion \(M_{\alpha}\) and an additional integral of motion \(G\), which are first- and fourth-order polynomials in momenta, respectively.

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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.