SEPARABILITY AND LAX PAIRS FOR HENON-HEILES SYSTEM

The Hamiltonian system corresponding to the (generalized) Henon-Heiles Hamiltonian H=1/2(p(x)2+p(y)2)+1/2Ax2+1/2By2+x2y+epsilony3 is known to be integrable in the following three cases: (A=B, epsilon=1/3); (epsilon=2); (B=16A, epsilon=16/3). In the first two the system has been integrated by making use of genus one and genus two theta functions. We show that in the third case the system can also be integrated by making use of elliptic functions. Finally, using the Fairbanks theorem, we find Lax pairs for each of the three integrable systems under consideration.