Версия от 04:28, 24 марта 2024; EducationBot(обсуждение | вклад)(Новая страница: «{{Английская Википедия/Панель перехода}} thumb|Contour plot of the Hénon–Heiles potential While at Princeton 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 nume...»)
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While at Princeton 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".[1] 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.
In the classical chaos community, the value of the parameter <math>\lambda</math> is usually taken as unity.
Since HHS is specified in <math>\R^2</math>, we need a Hamiltonian with 2 degrees of freedom to model it.
It can be solved for some cases using Painlevé analysis.
Hénon–Heiles system shows rich dynamical behavior. Usually the Wada property cannot be seen in the Hamiltonian system, but Hénon–Heiles exit basin shows an interesting Wada property. It can be seen that when the energy is greater than the critical energy, the Hénon–Heiles system has three exit basins. In 2001 M. A. F. Sanjuán et al.[3] had shown that in the Hénon–Heiles system the exit basins have the Wada property.