Hénon–Heiles system

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 that purpose they took 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.