{"title":"Compactification of the Energy Surfaces for \\(n\\) Bodies","authors":"Andreas Knauf, Richard Montgomery","doi":"10.1134/S1560354723040081","DOIUrl":null,"url":null,"abstract":"<div><p>For <span>\\(n\\)</span> bodies moving in Euclidean <span>\\(d\\)</span>-space under the influence of a\nhomogeneous pair interaction we\ncompactify every center of mass energy surface, obtaining a\n<span>\\(\\big{(}2d(n-1)-1\\big{)}\\)</span>-dimensional manifold with corners in the sense of Melrose.\nAfter a time change, the flow on this manifold is globally defined\nand nontrivial on the boundary.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"628 - 658"},"PeriodicalIF":0.8000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354723040081","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: 1
Abstract
For \(n\) bodies moving in Euclidean \(d\)-space under the influence of a
homogeneous pair interaction we
compactify every center of mass energy surface, obtaining a
\(\big{(}2d(n-1)-1\big{)}\)-dimensional manifold with corners in the sense of Melrose.
After a time change, the flow on this manifold is globally defined
and nontrivial on the boundary.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
