A note on the Hénon–Heiles problem

Abstract

The Hamiltonian for the Hénon–Heiles problem, H= (1/2)(p₁²+p₂²+q₁²+q₂²)+q₁²q₂ −(1/3) q₂³, 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.