Phase space transport in a symmetric Caldera potential with three index-1 saddles and no minima

Matthaios Katsanikas, Makrina Agaoglou, Stephen Wiggins, Ana M. Mancho

incompletemedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper correctly identifies the phase-space mechanism—heteroclinic intersections between the unstable manifolds of the upper UPOs and the stable manifold of the lower UPO, followed by guidance by the two branches of the lower UPO’s unstable manifold—and demonstrates it clearly with Lagrangian Descriptors on appropriate slices (y=0.84 and y=0) for E=2.821 . However, it provides a qualitative demonstration rather than a rigorous, assumption-complete proof. The model’s solution presents the correct mechanism at a theoretical level (NHIM/UPO tubes, codimension-1 conduits, generic transverse intersections), but contains an internal mismatch in Section (c) about which exit corresponds to “dynamical matching” (the paper defines matching as upper-right to LER and upper-left to RER, not same-side exits) . There is also a minor textual inconsistency in the paper regarding the presence/absence of a minimum in the central region .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript delivers a clear, well-motivated phase-space explanation of dynamical matching/non-matching using Lagrangian Descriptors. The figures and example trajectories convincingly identify heteroclinic lobes between the upper UPO’s unstable manifold and the lower UPO’s stable manifold, and the two-branch structure of the lower UPO’s unstable manifold that directs trajectories to LER or RER. Minor issues include consistency in the definition and illustration of “dynamical matching” at the chosen energy, and a small textual inconsistency regarding the presence of a minimum in the central region. These do not affect the core mechanism but warrant polishing for clarity.