Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.09809 |
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Sommario:
- An elliptic relative equilibrium (ERE) is a special solution of the planar $N$-body problem generated by a central configuration. Its linear stability depends on the eccentricity $e$ and the masses of the bodies. However, for $e>0$, the variational equations become non-autonomous and highly complex, particularly near $e=1$, where the system exhibits a singularity. This complicates the stability analysis as $e$ approaches one, making it challenging to derive a rigorous quantitative estimate for the stable region across $e\in[0,1)$. In this work, we address this problem. Using trace formulas for the non-degenerate Hamiltonian system of EREs, we establish an upper bound ensuring non-degeneracy for all $e\in[0,1)$. As key applications, we provide explicit stability estimates for the Lagrange, Euler, and regular $(1+n)$-gon EREs over the full range of eccentricity.