Nonlinear resonances and dynamic stochasticity

In the framework of classical theory of nonlinear oscillations, random or stochastic processes are considered. A problem of stabilizing the resonance by nonlinearity is discussed. The nature of randomness is connected with the continuity of phase space of a dynamic system. The initial conditions of the system motion are given in the form of infinite aperiodic succession of digits. This succession contains from the beginning all the future (past) random process along the tragectory in question. Some applications of the theory are presented: confinement of particles along the magnetic lines and fine structure of a nonlinear resonance