GENERIC EQUIDISTRIBUTION OF PERIODIC ORBITS FOR AREA-PRESERVING SURFACE MAPS

Rohil Prasad

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 that a C^∞-generic area-preserving surface diffeomorphism admits an equidistributed sequence of orbit sets (Theorem 1.1) and, as a corollary, provides a sequence of periodic orbits whose prefix-averages equidistribute; it does not assert that each periodic orbit in the sequence is individually equidistributed. The candidate solution incorrectly cites the paper as giving a sequence of simple periodic orbits with per-orbit equidistribution and then takes each orbit as an orbit set. That inference is unjustified and reverses the logical direction of the paper’s Corollary 1.4. Hence, the model’s argument is wrong even though the paper’s result establishes the desired property directly.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The work achieves a substantive advance by proving a generic equidistribution theorem for orbit sets of area-preserving surface diffeomorphisms using PFH spectral invariants and a deft variational argument. The strategy is well-motivated and clearly described, with careful attention to genericity and nondegeneracy. A few clarifications would improve readability and prevent misinterpretations (notably the difference between orbit-set equidistribution and per-orbit statements), but the mathematical content appears sound and valuable to the field.