2203.12966
The criticality of reversible quadratic centers at the outer boundary of its period annulus
D. Marín, J. Villadelprat
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The candidate solution accurately restates the paper’s main theorem on the criticality of the period function at the outer boundary for reversible quadratic centers and follows the same Roussarie/Écalle–compensator plus ECT/Chebyshev framework used by Marín–Villadelprat. It identifies the same bifurcation locus Γ_B (including the analytic arc D=G(F)), the same resonant strata (D=−1 and D=0), the same special points ((−2,2) and (G(4/3),4/3)), and argues via the same uniform Dulac-time asymptotics and principal-part control that yield the stated criticality bounds. No substantive deviations or contradictions were found.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
Technically strong and consistent with the established Roussarie framework, the work provides definitive criticality bounds and exact counts for the outer boundary in the reversible quadratic family. The arguments are careful and uniform across strata, including resonant cases. Minor improvements in explicitly stating hypotheses (center region), summarizing strata-dependent principal scales, and clarifying regularity assumptions would aid clarity.