# The Hénon-Heiles System

The Hénon-Heiles System

In 1964, Henon and Heiles introduced a model to study the motion of a star through a galaxy with a two-dimensional, non-integrable potential, the result of adding a perturbation to an integrable harmonic potential. This Demonstration shows a plot of the phase-space trajectory and the Poincaré map. This system is an often-cited example of chaotic dynamics.

In 1964, Henon and Heiles introduced a model to study the motion of a star through a galaxy with a two-dimensional, non-integrable potential, the result of adding a perturbation to an integrable harmonic potential. This Demonstration shows a plot of the phase-space trajectory and the Poincaré map. This system is an often-cited example of chaotic dynamics.

The equations of motion are =p, =p, =-x-2xy, and =-y-x+y, where and are the coordinates and and are the momenta. The energy is equal to .

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2

2

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p/2+p/2+x/2+xy+y/2-y/3

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2

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