Poincaré Section: Hénon-Heiles Hamiltonian

Hénon-Heiles Hamiltonian: H = ½(p_x²+p_y²) + ½(x²+y²) + x²y − y³/3. This 2D Hamiltonian has no known analytic solution but interpolates between integrable (E→0) and fully chaotic (E=1/6≈0.167) behavior.

Poincaré section: Record (y, p_y) whenever x=0 and p_x>0. For integrable orbits: closed curves (KAM tori). For resonant orbits: chains of islands (fixed points). For chaotic orbits: scattered dots filling the stochastic sea.

Click on the section to launch a new trajectory from that (y, p_y) point. Each color is a different orbit.