Choreographies require sectorwise C_n phase-matching in Fourier-decomposed dynamics, occurring only in single irreducible sectors or via exact degeneracy, while generic resonant motions are periodic but multi-trace.
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Superintegrability and choreographic obstructions in dihedral $n$-body Hamiltonian systems
Choreographies require sectorwise C_n phase-matching in Fourier-decomposed dynamics, occurring only in single irreducible sectors or via exact degeneracy, while generic resonant motions are periodic but multi-trace.