一般三体问题的第二种解

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2026-10-19 DOI:10.1134/S1560354726050059

Sergey V. Bolotin

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引用次数: 0

摘要

我们考虑平面三体问题，其中两个质量比第三个小得多。小体近碰撞的周期解用poincarcars第二种解命名。庞加莱给出了一个如何证明它们存在的想法，但没有给出实际的证明。完备的证明出现得要晚得多，而且只适用于受限的三体问题。我们将一般三体问题的二阶解问题简化为一个台球型问题的动力学研究，并说明了如何将庞加莱的论点转化为一个严格的证明。

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Poincaré Second Species Solutions of the General Three-Body Problem

We consider the plane three-body problem with two of the masses much smaller than the third. Periodic solutions with near collisions of the small bodies were named by Poincaré second species solutions. Poincaré gave an idea of how to prove their existence, but didn’t provide an actual proof. Complete proofs appeared much later and only for the restricted three-body problem. We reduce the problem of second species solutions of the general three-body problem to the study of dynamics of a billiard type problem and show how to transform the arguments of Poincaré into a rigorous proof.

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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.