Symmetric solutions of the $n$-body problem: a numerical study of Floquet multipliers and Morse indices
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866915630898216960 |
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| author | Berti, Diego Canneori, Gian Marco Ciccarelli, Roberto De Blasi, Irene Introna, Margaux Polimeni, Davide |
| author_facet | Berti, Diego Canneori, Gian Marco Ciccarelli, Roberto De Blasi, Irene Introna, Margaux Polimeni, Davide |
| contents | In this paper, we consider periodic solutions of the $n$-body problem that satisfy symmetry constraints, expressed through invariance under finite group actions. We focus on their stability properties and present algorithms specifically designed for the computation of Floquet multipliers and Morse indices. Numerical results are provided to illustrate our methods in both two and three dimensional configuration spaces, and for different choices on the number of bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetric solutions of the $n$-body problem: a numerical study of Floquet multipliers and Morse indices Berti, Diego Canneori, Gian Marco Ciccarelli, Roberto De Blasi, Irene Introna, Margaux Polimeni, Davide Dynamical Systems Numerical Analysis In this paper, we consider periodic solutions of the $n$-body problem that satisfy symmetry constraints, expressed through invariance under finite group actions. We focus on their stability properties and present algorithms specifically designed for the computation of Floquet multipliers and Morse indices. Numerical results are provided to illustrate our methods in both two and three dimensional configuration spaces, and for different choices on the number of bodies. |
| title | Symmetric solutions of the $n$-body problem: a numerical study of Floquet multipliers and Morse indices |
| topic | Dynamical Systems Numerical Analysis |
| url | https://arxiv.org/abs/2511.17234 |