2106.04925
NONINTEGRABILITY OF THE RESTRICTED THREE-BODY PROBLEM
Kazuyuki Yagasaki
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves meromorphic nonintegrability of the circular restricted three-body problem near each primary for all µ∈(0,1) by: (i) local scaling near a primary to a nearly integrable Hamiltonian, (ii) passage to Delaunay-type variables, (iii) verification of a Melnikov/Galoisian obstruction using a computable loop integral Ξ that is nonzero on a resonant torus, and (iv) application of a general criterion (Theorem 2.1) grounded in Ayoul–Zung/Morales–Ramis–Simó theory. The candidate solution mirrors this structure and reaches the same conclusions for the planar and spatial cases. Minor discrepancies are referencing errors (nonexistent equation/theorem numbers) and a distinct evaluation method (residue/contour vs. the paper’s explicit real integral), but these do not affect correctness.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The manuscript delivers a modern, effective proof of local meromorphic nonintegrability for CR3BP near each primary across all mass ratios, leveraging a robust Galoisian framework. The reductions and explicit calculations are clear and persuasive, and the result meaningfully advances a classical problem. Minor clarifications regarding assumptions and external dependencies would strengthen the presentation.