Shooting for collinear periodic orbits in the Helium model

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-17 DOI:10.1007/s00033-023-02120-8

Lei Zhao

引用次数: 1

Abstract

Abstract The frozen-planet periodic orbit of the classical collinear Helium model with negative energy is shown to exist by a simple shooting argument. This simplifies the approach established in Cieliebak et al. (Ann Inst H Poincaré Anal Non Linéaire 40:379–455, 2022). With this argument, it also follows that the algebraic count of the number of such orbits with a given negative energy is 1, as recently established in Cieliebak et al. (Nondegeneracy and integral count of frozen-planet orbits in helium, 2022. arXiv:2209.12634 ). The same argument also leads to the existence of other collinear periodic orbits of the classical collinear Helium model.

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在氦模型中寻找共线周期轨道

摘要通过一个简单的射击论证，证明了负能量的经典共线氦模型的冰冻行星周期轨道的存在。这简化了Cieliebak等人建立的方法(Ann Inst H poincar Anal Non linsamaire 40:379-455, 2022)。根据这一论点，也可以得出，具有给定负能量的这种轨道的代数计数为1，正如最近在Cieliebak等人(氦中冻结行星轨道的非简并和积分计数，2022)中所建立的那样。arXiv: 2209.12634)。同样的论点也导致了经典共线氦模型的其他共线周期轨道的存在。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.