{"title":"Rotations and Integrability","authors":"Andrey V. Tsiganov","doi":"10.1134/S1560354724060029","DOIUrl":null,"url":null,"abstract":"<div><p>We discuss some families of integrable and superintegrable systems in <span>\\(n\\)</span>-dimensional Euclidean space which are invariant under <span>\\(m\\geqslant n-2\\)</span> rotations. The invariant Hamiltonian <span>\\(H=\\sum p_{i}^{2}+V(q)\\)</span> is integrable with <span>\\(n-2\\)</span> integrals of motion <span>\\(M_{\\alpha}\\)</span> and an additional integral of\nmotion <span>\\(G\\)</span>, which are first- and fourth-order polynomials in momenta, respectively.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 6","pages":"913 - 930"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354724060029.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354724060029","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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