Unbounded solutions to a system of coupled asymmetric oscillators at resonance

The paper derives a precise stroboscopic (time-2π) map in action–angle variables where the radial update is ri(2π) = ri,0 − ∂iLi(θ0) + small and the angular update is θi(2π) = θi,0 + 2πn + (1/ri,0)(Li(θ0) + small). This structure is essential for the invariant-block construction and relies on the D+-property to ensure ∂iLi < 0 near a zero ω of L, hence uniform growth of r. The candidate solution, however, asserts the incorrect law ri(k+1) = ri(k) + Li(θ(k)) + error and then uses positivity of Li—rather than negativity of ∂iLi—to deduce growth. This misidentifies the governing quantity for radial growth and breaks the main logical step. The rest of the candidate’s outline (isochrony, saturation of φi, stroboscopic reduction, measure claim) broadly follows the paper’s strategy, but the core map and invariant-block argument are wrong.