摘要
A 3 x 3 discrete eigenvalue problem associated with the Lotka-Volterra hierarchy is studied and the corresponding nonlinearized one, an integrable Poisson map with a Lie-Poisson structure, is also presented. Moreover, a 2 x 2 nonlinearized eigenvalue problem, which also begets the Lotka-Volterra hierarchy, is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation.