Hénon–Heiles system

In 1964 they published an article titled "The applicability of the third integral of motion: Some numerical experiments".

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.

The Hénon–Heiles potential can be expressed as[2] The Hénon–Heiles Hamiltonian can be written as The Hénon–Heiles system (HHS) is defined by the following four equations: In the classical chaos community, the value of the parameter

In 2001 M. A. F. Sanjuán et al.[3] had shown that in the Hénon–Heiles system the exit basins have the Wada property.