This report is about the dynamics of the Hamiltonian systems with two degrees of freedom, in the presence of a low-frequency disturbance. It is proved that a low-frequency disturbance induces a stochastic instability. Besides, a low-frequency disturbance can stimulate the development of a parametric instability. This instability is a new mechanism of transformation of low-frequency oscillation energy to a energy of high-frequency oscillation. As examples of the parametric instability development in distributed systems, we have examined the possibility of the parametric amplification of the x-ray radiation emission in crystals and the possibility of the parametric amplification of the waves propagating in gyrotropic media.
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