在氦模型中寻找共线周期轨道

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

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引用次数: 1

摘要

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。

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Shooting for collinear periodic orbits in the Helium model

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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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

期刊介绍： The Journal of Applied Mathematics and Physics (ZAMP) publishes papers of high scientific quality in Fluid Mechanics, Mechanics of Solids and Differential Equations/Applied Mathematics. A paper will be considered for publication if at least one of the following conditions is fulfilled: The paper includes results or discussions which can be considered original and highly interesting. The paper presents a new method. The author reviews a problem or a class of problems with such profound insight that further research is encouraged. The readers of ZAMP will find not only articles in their own special field but also original work in neighbouring domains. This will lead to an exchange of ideas; concepts and methods which have proven to be successful in one field may well be useful to other areas. ZAMP attempts to publish articles reasonably quickly. Longer papers are published in the section "Original Papers", shorter ones may appear under "Brief Reports" where publication is particularly rapid. The journal includes a "Book Review" section and provides information on activities (such as upcoming symposia, meetings or special courses) which are of interest to its readers.