Hénon-Heiles Hamiltonian: H = ½(ẋ² + ẏ²) + ½(x² + y²) + x²y − y³/3. The Poincaré section records (y, ṗy) each time x = 0 with ẋ > 0. At low energy (E ≪ 1/6 ≈ 0.167), KAM tori dominate — trajectories trace closed curves. Near E = 1/6 the potential barrier is reached and most tori break, leaving a chaotic sea dotted with stable islands. This was a landmark 1964 paper showing that generic Hamiltonians are non-integrable.