SYMMETRY OF APPROXIMATE HAMILTONIANS GENERATED IN BIRKHOFF-GUSTAVSON NORMAL-FORM

Previous investigators have shown how the Birkhoff-Gustavson normal fo rm (BGNF) procedure can be used to develop an integrable Hamiltonian w hich approximates a nonintegrable Hamiltonian system. We discuss the s ymmetry properties of these approximate Hamiltonians and how a certain flexibility inherent to the BGNF procedure can be used to affect this symmetry. Because the BGNF procedure involves a transformation of the coordinates, the symmetry issue has been somewhat neglected due to it s complexity. The techniques we demonstrate here with the Henon-Heiles Hamiltonian are easily generalized for use in molecular Hamiltonians of arbitrary symmetry.