Measured by the lab
0.16666667
aidoesscience › Hénon–Heiles
Investigating · validationsHénon–Heiles · Poincaré section simulation
How does a smooth Hamiltonian system slide from order into chaos as its energy rises?
▶ Run the simulationSee the measured result
Known value
0.16666667
Relative error
7.21e-14
How the lab tests it
Integrate orbits of the Hénon–Heiles galactic potential and take a Poincaré section (their crossings of the plane x=0); a regular orbit pierces it on a smooth closed curve, a chaotic one scatters. Each orbit's Lyapunov exponent colours it blue (regular) or warm (chaotic).
What it looks for
the KAM scenario: at low energy nested invariant tori (regular), which progressively break into a chaotic sea as the energy climbs toward the escape energy 1/6
This simulation has a catalogued, oracle-checked result: The Hénon–Heiles escape energy 1/6 recovered from the bare equations of motion.