← Back to Labs

Hamiltonian Chaos & Poincaré Section

Hénon-Heiles System

H = ½(ẋ²+ẏ²) + ½(x²+y²)
   + λ(x²y − y³/3)

ẍ = −x − 2λxy
ÿ = −y − λ(x²−y²)

Parameters

Controls

Stats

Section points 0
Chaos level

About

The Hénon-Heiles system (1964) models galactic stellar dynamics. Below E≈1/12, orbits are regular KAM tori (closed curves in the Poincaré section). Near E≈1/6, chaos appears — tori break into cantori and scattered points. The KAM theorem (Kolmogorov-Arnold-Moser) guarantees persistence of many tori under small perturbations, but chaos invades at higher energy.