## Hénon-Heiles Equation

A nonlinear nonintegrable Hamiltonian System with

 (1) (2)

where
 (3) (4)

The energy is
 (5)

The above plots are Surfaces of Section for and . The Hamiltonian for a generalized Hénon-Heiles potential is

 (6)

The equations of motion are integrable only for
1. ,

2. ,

3. , and

4. .

References

Gleick, J. Chaos: Making a New Science. New York: Penguin Books, pp. 144-153, 1988.

Hénon, M. and Heiles, C. The Applicability of the Third Integral of Motion: Some Numerical Experiments.'' Astron. J. 69, 73-79, 1964.