2509.01377
On the Piecewise Holomorphic Systems with Three Zones
Carlos Vinícius das Neves Silva, Paulo Ricardo da Silva
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves Theorem C by a Möbius reduction to two parallel lines and a direct Melnikov/Wronskian computation that yields function bases with 5 (resp. 9) independent elements and hence at least 4 (resp. 8) simple Melnikov zeros, producing the stated limit cycles. The candidate solution asserts stronger, unproven ECT properties and a uniqueness claim, mis-cites the paper, and incorrectly downplays the role of imaginary parts. Thus, the paper’s result and proof are sound, while the model’s argument is incomplete/incorrect in key steps .
Referee report (LaTeX)
\textbf{Recommendation:} no revision
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper gives a clear, technically sound proof of lower bounds for the number of limit cycles in piecewise holomorphic systems with three zones when the discontinuity set is two tangent circles. The Möbius reduction to parallel lines, explicit Melnikov integrals, and Wronskian checks are appropriate and well executed. The results extend the toolkit for PWHS and complement recent literature. Minor editorial polishing could further aid readability.