Mathematical Physics

Continuation Geometry Resolves Apparent Branch Splitting in Unequal-Mass Three-Body Orbits

Authors: Ori Chamo, Yossi Eliaz

Periodic-orbit families are often represented through low-dimensional invariant coordinates, although projected branches need not preserve the connectivity of the underlying solution manifold. We use numerical continuation to examine the 135,445 unequal-mass planar three-body periodic orbits reported by Li, Li, and Liao, whose corrected scale-invariant period-angular-momentum representation was subsequently interpreted as two independent sets. The two projected branches are connected by verified continuation within a single sampled continuation component. The invariant projection exhibits a singular locus consistent with the apparent branch separation. High-precision Floquet calculations identify a +1 transition at one representative stability boundary and an opposite-Krein Hamiltonian-Hopf transition at another. Projection geometry and symplectic spectral geometry therefore provide complementary descriptions of the same periodic-orbit manifold.

Comments: 6 pages, English. PRL-format Letter followed by Supplemental Material.

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Submission history

[v1] 2026-08-19 21:27:04

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