具有任意质量的 n 体问题中可规整的共线周期解

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2024-09-11 DOI:10.1016/j.aim.2024.109947

Guowei Yu

{"title":"具有任意质量的 n 体问题中可规整的共线周期解","authors":"Guowei Yu","doi":"10.1016/j.aim.2024.109947","DOIUrl":null,"url":null,"abstract":"<div><p>For <em>n</em>-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the masses moving monotonically to the right and the other half monotonically to the left. When the masses satisfy certain equality condition, the solutions have extra symmetry. This also gives a new proof of the existence of Schubart orbit, when <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span>.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"457 ","pages":"Article 109947"},"PeriodicalIF":1.5000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regularizable collinear periodic solutions in the n-body problem with arbitrary masses\",\"authors\":\"Guowei Yu\",\"doi\":\"10.1016/j.aim.2024.109947\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For <em>n</em>-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the masses moving monotonically to the right and the other half monotonically to the left. When the masses satisfy certain equality condition, the solutions have extra symmetry. This also gives a new proof of the existence of Schubart orbit, when <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span>.</p></div>\",\"PeriodicalId\":50860,\"journal\":{\"name\":\"Advances in Mathematics\",\"volume\":\"457 \",\"pages\":\"Article 109947\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0001870824004626\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870824004626","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

对于具有任意正质量的 n 体问题，我们证明了对于质量的任意排序都存在可正则化的碰撞周期解，从同时发生的二元碰撞到另一组碰撞只需半个周期，其中一半质量单调地向右移动，另一半质量单调地向左移动。当质量满足某些相等条件时，解具有额外的对称性。这也给出了 n=3 时舒巴特轨道存在的新证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Regularizable collinear periodic solutions in the n-body problem with arbitrary masses

For n-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the masses moving monotonically to the right and the other half monotonically to the left. When the masses satisfy certain equality condition, the solutions have extra symmetry. This also gives a new proof of the existence of Schubart orbit, when $n = 3$ .

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.