General validity of surface-of-section placement heuristic based on monodromy norm

Ascertain whether placing the Poincaré surface of section at locations where the norm of the monodromy matrix is smallest generally improves local Poincaré map identification accuracy and reduces control effort, beyond the circular restricted three-body problem, and determine the conditions under which this guideline holds across different dynamical systems.

Background

The paper proposes and empirically supports a heuristic for choosing a Poincaré surface of section in the circular restricted three-body problem: identify the section where the monodromy matrix has the smallest norm, interpreted as the least sensitive region to perturbations. In their experiments on Lyapunov and halo orbits, the section with smaller monodromy norm produced more accurate SINDy-identified local Poincaré maps and substantially lower control cost.

While these results are compelling for the specific cases studied, the authors note that the broader question of whether this criterion generalizes to other systems remains unresolved. They explicitly flag this as an open question and suggest testing on different systems as a next step.