ENTROPY OF SINGULAR SUSPENSIONS.

Elias Rego, Sergio Romaña

correctmedium confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves the generic dichotomy for singular suspensions with countably many singularities (Theorem A) and supplies a zero-entropy criterion via the return-time function γ, then derives positivity from horseshoes by constructing minimal sets disjoint from the singular cross-sections. The candidate solution establishes the same dichotomy using Abramov-type reasoning and a symbolic “avoidance lemma” within a horseshoe, then uses hyperbolic continuation to obtain an open dense set. The arguments align in conclusions and hypotheses, while differing in technique. Minor formal details (ergodic decomposition, precise use of Abramov’s formula across the non-singular region, and the symbolic counting in the avoidance lemma) should be made explicit, but do not affect the overall correctness.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper convincingly establishes a generic preservation (and characterization) of entropy positivity under singular suspensions, using a clean topological route and a sharp measure-theoretic criterion. The results are timely and relevant, with additional applications to expansive and Anosov dynamics. Clarifying the open-dense construction for Theorem A in the general (non-conservative) setting with explicit references would further strengthen the presentation. Otherwise, the arguments appear correct and well-motivated.