Chaos and Regularity in the Double Pendulum with Lagrangian Descriptors

The candidate reproduces the paper’s nondimensional Hamiltonian, mass/length parametrization, and equations of motion (including B−1 and the θ′, p′ form), uses the identical Poincaré section Σ(H0) = {H = H0, θ2 = 0, βp2 − αp1 cosΔθ > 0}, and applies the same LD-based chaos indicator Sn_L with p = 1/2 and an adaptive histogram-valley threshold on log-indicator values. These are the core methodological steps in the paper (Hamiltonian and parametrization; LD definition and p=1/2; section Σ(H0), neighbors, and histogram threshold) and match the logic used to establish the paper’s findings about C(α,σ,H0), including the grid αi=2^i, σj=2^j and the energy schedule. Differences are numerical (e.g., τ and neighbor spacing), the θ1 symmetry restriction, and incomplete scaling to the full 9×9×170 runs, which explain the demo’s weaker fits compared to the paper’s exponential trends at high energy. None of these differences contradict the paper; they mainly affect statistical power and accuracy. Thus, both are methodologically consistent; the model is incomplete computationally but not conceptually at odds with the paper’s argument.