2103.14834
Dynamical System of a Quadratic Stochastic Operator with Two Discontinuity Points
Sh.B. Abdurakhimova, U. A. Rozikov
wronghigh confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem 8(6) misclassifies the endpoint x(0)=1/3 as belonging to the 1-basin when, by the operator’s own definition f(x) uses the left branch at x=1/3 and hence converges to 0 for a<1/2. The model’s solution correctly flags and fixes this boundary error and otherwise provides a clean, monotonicity-based proof of items (1)–(9).
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper contains substantial, largely correct regime-by-regime conclusions for a piecewise-quadratic QSO, but it has a concrete endpoint error (Theorem 8(6)) and relies on sketchy references to earlier proofs for the most general case. With corrected endpoint statements and full, explicit proofs for Theorem 8’s invariant bands and basins, the contribution would be solid and instructive for the QSO community.