NOTE ON THE HENON-HEILES PROBLEM

The Hamiltonian for the Hénon-Heiles problem, H = (1/2)(p 12 + p22 + q12 + q22) + q12 - (1/3)q 23, is a particular example of time-independent Hamiltonians for two-dimensional oscillator systems with third degree anharmonicity. It has been used as a model for galactic motion. There has been much discussion of the possible existence of an integral other than the Hamiltonian. In this note we show that the Hénon-Heiles Hamiltonian in particular and the class in general does not possess an invariant series which is explicitly time-independent other than the Hamiltonian itself. © 1980 American Institute of Physics.