A note on the Hénon-Heiles problem

Details A note on the Hénon-Heiles problem A note on the Hénon-Heiles problem

Jan 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980jmp....21...38l&link_type=abstract

Journal of Mathematical Physics, Volume 21, Issue 1, pp. 38-43 (1980).

Mathematics

Mathematical Physics

3

Scientific paper

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.

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