Local Inverse Measure-Theoretic Entropy for Endomorphisms

Eugen Mihailescu, Radu B. Munteanu

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper establishes the identity h_f^-(µ)=h_f(µ)−F_f(µ) for inverse entropy defined via partitions under explicit hypotheses (zero boundary property, bounded Jacobian, finite entropy), and derives only an inequality for Bowen-ball inverse entropy in general. The model’s proof aims to obtain the full Bowen-ball identity by replacing the paper’s zero boundary property with a uniform-continuity-on-large-set argument, but it does not guarantee that all points inside each forward Bowen ball remain in the continuity region at the relevant times. This missing uniformity breaks the key distortion estimate for J^{(n)} on Bowen balls. Consequently, the model’s Step 3 has a gap and its conclusion is not justified without the paper’s additional hypothesis.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper presents a well-structured development of inverse local entropy notions for endomorphisms and rigorously relates them to folding entropy and forward entropy. The core technical contribution—uniform distortion control for Jacobians on Bowen balls via the zero boundary property—is sound and addresses a real obstacle. Some expository refinements would enhance accessibility, but the results are correct and valuable to the field.