Hénon–Heiles system

The Hénon-Heiles system is a nonlinear mathematical model that describes the motion of a particle in a two-dimensional potential. It was introduced in 1964 by astronomers Michel Hénon and Carl Heiles to study the dynamics of stars in a galaxy. Still, it has become an example in the study of nonlinear dynamical systems, Hamiltonian chaos, and celestial mechanics.

While at Princeton University in 1962, Michel Hénon and Carl Heiles worked on the non-linear motion of a star around a galactic center with the motion restricted to a plane. In 1964, they published an article titled "The applicability of the third integral of motion: Some numerical experiments". Their original idea was to find a third integral of motion in a galactic dynamics. For this purpose, they considered a simplified two-dimensional, nonlinear, rotational symmetric potential and found that the third integral existed only for a limited number of initial conditions.

In the modern perspective, the initial conditions that do not have the third integral of motion are called chaotic orbits.