{"title":"Distance Estimates for Action-Minimizing Solutions of the \\(N\\)-Body Problem","authors":"Kuo-Chang Chen, Bo-Yu Pan","doi":"10.1134/S1560354723040044","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we provide estimates for mutual distances of periodic solutions for the Newtonian <span>\\(N\\)</span>-body problem.\nOur estimates are based on masses, total variations of turning angles for relative positions, and predetermined upper bounds for\naction values. Explicit formulae will be proved by iterative arguments.\nWe demonstrate some applications to action-minimizing solutions for three- and four-body problems.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 4","pages":"561 - 577"},"PeriodicalIF":0.8000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354723040044","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
In this paper we provide estimates for mutual distances of periodic solutions for the Newtonian \(N\)-body problem.
Our estimates are based on masses, total variations of turning angles for relative positions, and predetermined upper bounds for
action values. Explicit formulae will be proved by iterative arguments.
We demonstrate some applications to action-minimizing solutions for three- and four-body problems.
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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