2108.13312
Bifurcation of closed orbits from equilibria of Newtonian systems with Coriolis forces
Anna Gołȩbiewska, Ernesto Pérez-Chavela, Sławomir Rybicki, Antonio J. Ureña
correctmedium confidenceCounterexample detected
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The candidate reproduces the core spectral classification and the existence/nonexistence statements of Theorems 3.1–3.3 (formulas for T±, regions R0,R1–R4, the spatial resonance T0=2π/√β3, and the role of the Brouwer index), in line with the paper’s computations via the ST-matrix and bifurcation numbers γ2,γ3 . However, the model asserts that a branch also emanates on the boundary (β1,β2)∈∂R0\C, claiming a nonzero degree jump there. This contradicts the paper: Proposition 8.1(ii) shows the Morse index does not change across T± on ∂R0\C, hence γ2=0 and no bifurcation is guaranteed; an explicit counterexample at (−1,−1)∈∂R0 has no nontrivial periodic solutions at all . Thus the paper’s results are correct and the model overclaims on the boundary case.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper offers a robust, explicit, and general framework for detecting global branches of periodic orbits in gyroscopic Newtonian systems. Its degree-theoretic method handles degeneracies and yields concrete bifurcation numbers tied to spectral data. The exposition is clear and careful about delicate boundary regimes, even providing a counterexample. Minor structural enhancements could further improve accessibility.