NEW ASPECTS OF INTEGRABILITY OF GENERALIZED HENON-HEILES SYSTEMS

The class of so-called Henon-Heiles systems is slightly broadened by allowing for the existence of non-standard Hamiltonians. The extra parameter in the equations of motion is shown to give rise to a generalization of the three known integrability cases. In addition, three degenerate cases are detected, characterized by a partial decoupling of the equations. For these cases, we still obtain two independent first integrals, but their involutiveness can only be understood in terms of a non-standard Poisson structure.