Shooting for collinear periodic orbits in the Helium model

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 th...

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Veröffentlicht in:Zeitschrift für angewandte Mathematik und Physik 2023-12, Vol.74 (6), Article 227
1. Verfasser: Zhao, Lei
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-023-02120-8