BI-ASYMPTOTIC c-EXPANSIVITY

Rohit Nageshwar, Abdul Gaffar Khan, Tarun Das

correcthigh confidence

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

Audit review

The uploaded paper proves a spectral decomposition for bi-asymptotically c-expansive, surjective maps with shadowing via a clear chain of lemmas: (i) CR(f)=Ω(f)=Per(f) using asymptotic expansivity results, (ii) a stable/unstable intersection lemma, (iii) openness and finiteness of basic sets, and (iv) a periodic-point-based cyclic decomposition with mixing of an iterate (Theorem 1.1 and Lemmas 5.1–5.6) . The model solution, by contrast, contains critical gaps and mis-citations: it (a) incorrectly attempts to prove CR(f)=Ω(f) from shadowing alone (not true in general and not how the paper proceeds), (b) posits an unproven “uniform α” separation lemma that does not appear in the paper, and (c) sketches a gcd-of-chain-lengths decomposition not used by the paper and unsupported under the given hypotheses. Hence the paper’s argument is correct and complete for the stated result, while the model’s is not.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper extends spectral decomposition to a new expansivity class for continuous surjections with shadowing. The proof strategy is well chosen, building on asymptotic expansivity to identify the relevant dynamical core and then exploiting stable/unstable intersections to establish openness, finiteness, and a periodic-point-based cyclic structure with mixing of an iterate. Some proofs could benefit from additional exposition, but the results appear correct and meaningful.