Computer-assisted proof
Marchal's conjecture and the $P_{12}$ family
The $P_{12}$ family connects the Lagrange equilateral solution with the figure-eight choreography in the equal-mass three-body problem.
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Mathematical context
Marchal's conjecture predicts a continuous family of periodic solutions in the three-body problem joining the Lagrange equilateral triangle solution to the figure-eight choreography. This family is traditionally denoted by $P_{12}$.
The computer-assisted proof combines symmetry reduction, spectral representations, interval arithmetic and validated continuation. The goal is not only to compute the family numerically, but to certify its existence with mathematically rigorous error bounds.
Related publication
- R. Calleja, O. Hénot, C. García-Azpeitia, J.-P. Lessard and J. D. Mireles James, A Computer-Assisted Proof of Marchal's Conjecture in the Three-Body Problem.