Distance Estimates for Action-Minimizing Solutions of the \(N\)-Body Problem

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI:10.1134/S1560354723040044

Kuo-Chang Chen, Bo-Yu Pan

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.

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一类（N）体问题的最小作用解的距离估计

本文给出了牛顿体问题周期解相互距离的估计。我们的估计是基于质量、相对位置的转向角的总变化以及作用值的预定上限。显式公式将通过迭代论证来证明。我们展示了一些应用于三体和三体问题的行动最小化解决方案。

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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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.