Adiabatic deformations of integrable two-frequency Hamiltonians

The paper discusses a mechanism of excitation and control of two-frequency oscillations in the integrable Hamiltonian systems. It is close to the autoresonant technique for controlling the amplitude of nonlinear modes. Autoresonance is usually associated with single frequency mode excitations due to the synchronization and phase lock of various nonlinear modes with the driving force. Despite this we propose a model of multifrequency autoresonance which occur in completely integrable systems. This phenomenon is due to a number stable invariant tori governed by integrals of motion of the integrable system. The basic autoresonant effect of phase locking appears here as Whitham deformations of the invariant tori. This provides also a possibility to transfer a certain initial n-periodic motion to a given m-periodic motion as a final state.