2409.03310
NON-UNIFORM COCYCLES FOR SOME UNIQUELY ERGODIC MINIMAL DYNAMICAL SYSTEMS ON CONNECTED SPACES
Wanshan Lin, Xueting Tian
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
Case (II) in the model matches the paper’s Theorem B (factor onto an irrational rotation, pull back Lenz’s non-uniform 2x2 cocycle, then lift dimension). But in Case (I) the model overstates the result: Lin–Tian prove existence only for dimensions m ≥ p under the additional hypothesis Q^e_{f^p}(X) ≠ X, supplied by Theorem D for class (I), not “for every m ≥ 2.” The model omits this Q^e-condition and claims the stronger m ≥ 2 conclusion, which is unsupported by the paper (see Theorem C and D ).
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript gives a clear, structured advance on Walters's question by resolving a broad two-class swath of uniquely ergodic minimal systems on connected spaces and pinpointing an intriguing open third class. The proofs are technically sound, leveraging equicontinuous factors, Lenz's construction, and a careful measure-theoretic criterion Q\^e\_{f\^p}(X) ≠ X. A few expository clarifications would further strengthen accessibility.