AN APPROACH TO THE INTEGRABILITY OF HAMILTONIAN-SYSTEMS OBTAINED BY REDUCTION

A hierarchy of finite-dimensional integrable Hamiltonian systems can be obtained in a straightforward way by restricting a hierarchy of integrable evolution equations to the invariant subspace of their recursion operator. The independent integrals of motion and Hamiltonian functions for these Hamiltonian systems can be constructed by using the recursion formula and can be shown to be in involution. So these Hamiltonian systems are completely integrable in the sense of Liouville and commute with each other.