Abstract
We examine the case when equally sized small moons arrange themselves on the vertices of a regular n-gon for n≥ 7. For n ≥ 4, there are at least 3 pure imaginary characteristic exponents, each of which has multiplicity = 1, a surprising result that makes it possible to apply the Lyapunov center theorem to verify the existence of some periodic perturbations. For sufficiently large n, when the regular n-gon is the unique central configuration, the number of families of periodic perturbations is at least equal to 2n − ⌊(n + 1)/4⌋, where ⌊x⌋ is the greatest integer less than or equal to x.
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Pascual, F.G. On Periodic Perturbations of Uniform Motion of Maxwell's Planetary Ring. Journal of Dynamics and Differential Equations 10, 47–72 (1998). https://doi.org/10.1023/A:1022688312203
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DOI: https://doi.org/10.1023/A:1022688312203