MULTI-HAMILTONIAN STRUCTURES FOR A CLASS OF DEGENERATE COMPLETELY INTEGRABLE SYSTEMS

In this paper, a class of degenerate (i.e., associated to a degenerate Poisson structure) completely integrable systems is studied which gen eralizes the so-called odd and even master systems introduced and stud ied by Mumford and by Vanhaecke. It is shown that all these completely integrable systems, called the generalized master systems, admit a mu lti-Hamiltonian formulation, and a systematic construction of this mul ti-Hamiltonian structure is described. (C) 1996 American Institute of Physics.