2212.05467
Invariant cones for strange attractors of Lozi, Hénon and Belykh type maps
D. A. Grechko, V. N. Belykh, N. V. Barabash
wronghigh confidenceCounterexample detected
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem 1 states an unstable cone Ku = {0 < u2/u1 < λ} under d(x) < −2(1 + λ), but its own eigenvector bounds put the unstable slope on G− in (λ, 2λ) and its figure lists the edge (1, 2λ), contradicting (8). Hence Ku as stated is not forward invariant on G−, exactly as the model’s counterexample shows. The minimal fix is Ku = {0 < u2/u1 < 2λ} (and a uniform gap on G− for uniform expansion) .
Referee report (LaTeX)
\textbf{Recommendation:} reject
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The main cone-field assertion misstates the unstable cone (upper bound λ instead of 2λ), contradicting the paper’s own eigenvector bounds and figure, and invalidating forward invariance on G−. While likely a correctable slip, the error affects the core hyperbolicity claim and later applications, and the paper also omits a uniform margin on d(x) if uniform expansion is intended. These issues should be fixed before publication.