Hamiltonian Chaos — Poincaré Section

Hénon-Heiles system: order, KAM tori, and chaos

System

Hénon-Heiles:
H = ½(px²+py²+x²+y²) + λ(x²y − y³/3)

Click the canvas to launch a trajectory. Each point is plotted when y=0 (py>0) — a Poincaré section.

Below E≈1/6: integrable KAM tori (closed curves). Near E=1/6: chaos sets in — invariant tori dissolve into a chaotic sea.
Click on canvas to add trajectories at that (x, px) position