chapter  12
18 Pages

Galactic-Type Potentials and the He´non-Heiles System

The work of He´non and Heiles on galactic motion (He´non and Heiles, 1964) is

the first complete work proving the existence of chaos in galaxy formations. From

its first appearance in the Astronomical Journal (1964), it provided considerable evi-

dence of the existence of chaotic motions in galaxies. The work by He´non and Heiles

started as a computer experiment in order to explore the existence and applicability

of the third integral of galactic motion. Earlier, in 1956, George Contopoulos (Con-

topoulos, 1956) started a pioneering work on galactic motion and renewed the in-

terest on the third integral of motion (Contopoulos, 1960). Contopoulos explored

the box-like paths of a body in a galactic potential and found that the orbits in the

meridian plane of an axisymmetric galaxy are like Lissajous1 figures (Contopoulos,

1965). Contopoulos expected the orbits to be ergodic and fill all the space inside the

energy surface (Contopoulos, 2002). Instead, he found that the orbits did not fill all

the available space, but instead filled curvilinear parallelograms, like deformed Lis-

sajous figures. According to his writings he could prove later (Contopoulos, 1960)

that such orbits can be explained qualitatively and quantitatively by a formal third

integral of motion. The work of Contopoulos and He´non-Heiles was a result of what

we call computer experiments. This new type of experiments gave new directions

to various scientific fields, including astronomy. The computer results were some-

times surprising, and often contradicting existing theories. Contopoulos (1958) used

a computer in Stockholm Observatory in 1958, and He´non and Heiles (1964) used a

computer at Princeton University from 1962 to 1963.