Global continuation in the central mass

Determine whether a global branch in the central mass parameter joins the polyhedrally symmetric periodic-solution families constructed for large central mass to the corresponding periodic-solution families of the classical n-body problem at zero central mass.

Background

The paper constructs symmetric periodic motions by perturbing from the limit of infinite central mass, equivalently from inverse central mass parameter ε=0. It contrasts these solutions with polyhedrally symmetric periodic solutions known for the classical n-body problem, corresponding to central mass μ=0. The local perturbative construction does not determine whether these two families belong to a single global continuation branch as μ varies.

References

Whether a global branch in μ joins the two families is beyond a perturbative construction of this kind, and it is the question we plan to take up in a sequel to this paper.

— Platonic constellations of periodic motions in the $(n + 1)$-body problem  (2609.10242 - Constantineau et al., 9 Sep 2026) in Introduction, paragraph “Relation to the global methods”