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 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.
| Author: | Lei ZhaoGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1096611 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/109661 |
| ISSN: | 0044-2275OPAC |
| ISSN: | 1420-9039OPAC |
| Parent Title (German): | Zeitschrift für angewandte Mathematik und Physik |
| Publisher: | Springer Science and Business Media LLC |
| Type: | Article |
| Language: | English |
| Date of first Publication: | 2023/10/17 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/12/01 |
| Tag: | Applied Mathematics; General Mathematics; General Physics and Astronomy |
| Volume: | 74 |
| Issue: | 6 |
| First Page: | 227 |
| DOI: | https://doi.org/10.1007/s00033-023-02120-8 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Analysis und Geometrie | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung |
