Shooting for collinear periodic orbits in the Helium model

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Zeitschrift fur Angewandte Mathematik und Physik 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

Zeitschrift fur Angewandte Mathematik und Physik 数学-应用数学

CiteScore

2.90

自引率

10.00%

发文量

216

审稿时长

6-12 weeks

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