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

2025/11/21 by Diego Berti, Berti, Diego, Gian Marco Canneori +9
Engineering · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems #Space Satellite Systems and Control #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.2511.17234

openalex publication_date 2025/11/21 · openalex created_date 2025/11/25 · openalex updated_date 2026/07/28

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.

Citations

• Equivariant optimisation for the gravitational n-body problem: a computational factory of symmetric orbits
• Symmetries and periodic orbits for the n-body problem: about the computational approach
• From the Lagrange polygon to the figure eight I: Numerical evidence extending a conjecture of Marchal
• An Index theory for asymptotic motions under singular potentials
• Oscillatory motions for the restricted planar circular three body\n problem
• Platonic Polyhedra, Topological Constraints and Periodic Solutions of the Classical N-Body Problem
• Linear Stability of the Elliptic Lagrangian Triangle Solutions in the Three-Body Problem

Related

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• Periodic Solutions with Singularities in Two Dimensions in the n-body Problem