On complete integrability of a hierarchy of finite-dimensional Hamiltonian systems

A hierarchy of Hamiltonian systems obtained from the Lax pair of KdV hierarchy under the constraint condition on potentialu = q, q is presented. The independent integrals for these Hamiltonian systems are constructed by using recursion operator and shown to be in involution. Thus this hierarchy of Hamiltonian systems is completely integrable in the sense of Liouville, and they commute with each other.This project is supported by the National Natural Science Foundation of China.