State dependent delay maps: numerical algorithms and dynamics of projections.

J.D. Mireles James, Francis Motta, Vincent Naudot

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper defines K0, K1, K2 and the operator øz on C0,`0([0,1/2]) and proves that for |ε| ≤ min{1/(2K2), 1/(τ`K1)} the map is a contraction with constant ≤ 1/2, so it has a unique fixed point Ψε(z); completeness of the metric space is asserted, and the Half‑Stroboscopic map is thus well-defined . The candidate reproduces the same steps (self-map, contraction estimate d(øz(w1), øz(w2)) ≤ (ε τ ` K1 / 2) d(w1,w2), and completeness) and invokes Banach’s fixed-point theorem; the proof is essentially the same as the paper’s, with slightly stronger-than-necessary conditions in Step 1 and a fully written completeness argument.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The key contraction mapping result is correct and sufficient for defining the Half–Stroboscopic map. The candidate solution faithfully mirrors the paper’s proof and strengthens exposition by supplying a brief completeness argument. Minor editorial improvements—separating the roles of the ε-bounds and explicitly stating the Lipschitz implications—would increase readability. Overall, the mathematics is sound and well within the standards for a solid specialist contribution.