2107.11438
Explicit Solutions and Stability Properties of Homogeneous Polynomial Dynamical Systems via Tensor Orthogonal Decomposition
Can Chen
correcthigh 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 1 derives an explicit solution for x'(t) = A x(t)^{k-1} when A is orthogonally decomposable, by diagonalizing the vector field in the Z-eigenbasis and solving n decoupled scalar ODEs via separation, including the precise maximal interval and blow‑up criterion. The candidate solution follows the same decomposition, obtains the identical closed form, proves maximality/blow‑up in the same way, and adds a standard C^1-Lipschitz uniqueness justification. No substantive discrepancies found.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper’s core result is correct and clearly presented for a well-defined class (orthogonally decomposable tensors). The proof matches the candidate solution step-for-step. Minor editorial/rigor enhancements (explicit IVP uniqueness citation, branch/domain clarifications) would further strengthen the presentation. The contribution is specialized but useful for analysts working with tensor-structured nonlinear systems.