Phase Space (x, ẋ) — Poincaré Section y=0
Real Space Trajectory (x, y)
The Hénon-Heiles system (1964) models stellar motion in a galactic potential:
H = ½(ẋ²+ẏ²) + ½(x²+y²) + x²y − y³/3. At low energy, KAM tori survive as closed curves
in the Poincaré section — the system is near-integrable. As energy approaches E≈1/6≈0.167,
tori break apart and chaotic seas fill phase space. Drag the energy slider to watch the
transition from regularity to chaos.