In this paper, we study time-periodic perturbation of classical systems
with two degrees of freedom. A transition chain is established,
by passing through small neighborhood of double resonant point,
to connect any two cohomology classes corresponding to resonant
frequencies. Applying the result to nearly integrable Hamiltonian
systems with three degrees of freedom, one obtains a transition
chain along which one is able to construct diffusion orbits suggested
by Arnold in [A66].