Soft-mode oscillations of canonical momenta in a hamiltonian system

The Hamiltonian proposed previously is further studied. It is shown that the limit cycles of the real amplitudes of the interacting nonlinear oscillators may lose stabilities and become 2-tori owing to the re-excitation of the linear frequencies of the oscillators, which is attributed to the coupling perturbation of another kind of modes. From this as well as other authors results it is conjectured that the coupling between the moment equations of hydrodynamics may play a critical role in Ruelle-Takens route, and the picture of transition to turbulence is conceived as an adjusted motion attracted on two 2-tori