Hamiltonian chaos revealed through surface-of-section mapping. Each orbit's crossing of y=0 plotted as a single point.
H = ½(px²+py²) + ½(x²+y²) + x²y - ⅓y³
Hénon-Heiles (1964): test of galactic orbit integrability. At low E, KAM tori dominate (closed curves). Near E=1/6≈0.167, chaos spreads across phase space (island chains, stochastic sea).