Exact stationary solutions of stochastically excited and dissipated integrable Hamiltonian systems

The integrability and resonant property of a modified Hamiltonian system conditions exact stationary solutions for stochastically excited and dissipated integrable systems. Double summation Wong-Zakai correct terms are used to modify the Hamiltonian system. A nonintegrable system is solved using a Hamiltonian functional. The integrable system is solved by a functional of n independent motion integrals in the modified case.