2009.08971
Dynamics and structural stability of piecewise smooth dynamical systems presenting a double discontinuity
Guilherme Tavares da Silva, Ricardo Miranda Martins
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The candidate reproduces the paper’s blow-up computation for a double discontinuity, deriving the induced field under φ1(x,θ,r)=(x,r cosθ,r sinθ) and obtaining the slow–fast form ẋ=wi, r θ̇=qi cosθ−pi sinθ, ṙ=pi cosθ+qi sinθ, exactly as in equations (14)–(16) of the paper, with the reduced and layer systems at r=0 and t=rτ matching verbatim Theorem 4.1 on the cylinder stripes Si, with all functions evaluated at (x,0,0) . The only omission is the external justification that the stripe-boundary discontinuities are regular (the paper cites an external source for this), but this does not affect the derivation of the displayed systems.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The core theorem is derived cleanly via a cylindrical blow-up, converting an ill-posed Filippov configuration into a tractable slow–fast system on a cylinder. The approach is sound and aligns with established singular perturbation methods. Minor improvements would further strengthen clarity, particularly around boundary regularity and explicit evaluation points.