Resilience of Dynamical Systems

Hana Krakovská, Christian Kuehn, Iacopo P. Longo

correctmedium confidence

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

Audit review

The paper’s Proposition 4.13 states exactly the two claims to be proved—2·DT(A) ≤ Lw(A), and Lv(A,C) ≤ Lv(A, B_{DT(A)}(A)) = 1—and gives a brief proof outline relying on the definitions of latitude in width and distance to threshold and on the openness of the basin of attraction; see Definition 4.1, Definition 4.3, Proposition 2.4, and Proposition 4.13 in the uploaded paper . The candidate solution reaches the same conclusions via a slightly different but correct route: it spells out the openness of the basin, gives a full boundary-crossing argument to show B_{DT(A)}(A) ⊂ B(A), and handles the DT(A)=∞ case explicitly. Both are correct and consistent with the paper’s definitions and results (also using Definition 4.9 for Lv) .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

Proposition 4.13 is correct and useful as a clear link between three standard basin-shape indicators. The argument is elementary yet tidy. The exposition would benefit from supplying the short boundary-crossing proof for B\_{DT}(A) ⊂ B(A) and from explicitly noting the measure-theoretic domain for Lv in the DT(A)=∞ case. Otherwise, the section is clear and consistent with the earlier definitions and assumptions.