SURFACES OF LOCALLY MINIMAL FLUX

R. S. MacKay

correctmedium confidence

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

Audit review

The paper explicitly states that closed surfaces through minimising and minimax (p,q)-periodic orbits or through minimising advancing heteroclinic orbits generically have local recrossings and thus cannot be locally flux-minimising, invoking the no-local-recrossing criterion for locally minimal flux surfaces (Theorem 1) and giving illustrative arguments/figures rather than a detailed proof . The candidate solution supplies a rigorous local Poincaré-section construction of recrossings near hyperbolic minimax periodic orbits and advancing heteroclinics that aligns with the paper’s conclusions. Minor gaps (e.g., an under-justified appeal to algebraic intersection number zero in a local disc) do not affect the overall correctness. Hence both are correct, with different proof styles.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript consolidates and extends the understanding of locally minimal flux barriers, giving clear criteria and insightful applications to periodic and heteroclinic structures. The central observations about unavoidable local recrossings near non-degenerate minimax periodic orbits and advancing heteroclinics are correct and useful. However, these sections are expository and would benefit from short formal proofs (e.g., via Poincaré maps and the lambda-lemma) to make the paper a definitive reference.