Hamiltonian Chaos — Poincaré Section
Hénon-Heiles system: order, KAM tori, and chaos
System
Energy E:
0.12
λ (nonlinearity):
1.0
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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