NON-INTEGRABILITY OF GENERALIZED YANG-MILLS HAMILTONIAN SYSTEM

We show that the generalized Yang-Mills system with Hamiltonian H = 1/2(y(1)(2) + y(2)(2)) + 1/2(ax(1)(2) + bx(2)(2)) + 1/4cx(1)(4) + 1/4dx(2)(4) + 1/2ex(1)(2)x(2)(2) is meromorphically integrable in Liouvillian sense(i.e., the existence of an additional meromorphic first integral) if and only if (A) e = 0, or (B) c = d = e, or (C) a = b, e = 3 c = 3 d, or (D) b = 4a, e = 3c, d = 8c, or (E) b = 4a, e = 6c, d = 16c, or (F) b = 4a, e = 3d, c = 8d, or (G) b = 4a,e = 6d,c = 16d. Therefore, we get a complete classification of the Yang-Mills Hamiltonian system in sense of integrability and non-integrability.