3D Printing of Invariant Manifolds in Dynamical Systems

Patrick R. Bishop, Summer Chenoweth, Emmanuel Fleurantin, Alonso Ogueda-Oliva, Evelyn Sander, Julia Seay

correctmedium confidence

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

Audit review

The paper and the model both use the parameterization method to construct a local 2D stable manifold and then sweep its boundary via the flow to obtain a global surface, mitigating stretching by arclength-based time reparameterization. The homological equations, non-resonance assumptions, and local-to-global identity W^s(p)=⋃_{t≤0} φ_t(W^s_loc(p)) match. The model adds useful sign conventions for backward-time sweeping and concrete meshing/thickening safeguards; the paper states the arclength rescaling with a forward-time sign but elsewhere indicates backward integration for stable manifolds, a minor omission clarified by the model. Overall, they are methodologically aligned, with the model providing extra implementation detail.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript accurately conveys a practical and reproducible pipeline for computing, visualizing, and 3D printing invariant manifolds. It is grounded in standard theory (stable manifold theorem, parameterization method) and provides an effective arclength-based strategy for global growth. Minor clarifications—especially the sign convention for backward-time arclength integration in the stable case—and a few concrete meshing guidelines would strengthen clarity and reproducibility without altering the core contribution.