Poincaré Section — Hénon-Heiles

Hénon-Heiles Hamiltonian: H = ½(px²+py²) + ½(x²+y²) + x²y − y³/3. At low energy, KAM tori survive (closed curves in section). Increase energy toward chaos threshold E≈1/6 to see tori dissolve into scattered points. Section records when y=0, py>0.

Phase space trajectory (x, y)
Poincaré section (x, px) when y=0, ṗy>0
Crossings: 0