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arXiv · 2511.17234

Symmetric solutions of the $n$-body problem: a numerical study of Floquet multipliers and Morse indices

Diego Berti·Gian Marco Canneori·Roberto Ciccarelli·Irene De Blasi·Margaux Introna·Davide Polimeni
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Abstract

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.

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Diego Berti, Gian Marco Canneori, Roberto Ciccarelli, Irene De Blasi, Margaux Introna, Davide Polimeni. 2025-11-21. Symmetric solutions of the $n$-body problem: a numerical study of Floquet multipliers and Morse indices. https://arxiv.org/abs/2511.17234

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