Slipushenko S. Intermittency peculiarities in low chaotic physical systems

The thesis is devoted to studying of the properties of dissipative and Hamiltonian maps with non-differentiable singularities. The new intermittent stationary states are found in these systems. It is proved, that these new dynamical modes have self-similarity properties. The scaling exponent depends on the map parameters and may vary in a wide range in case of dissipative systems. The conditions when the trajectories do not contain any chaotic phases are obtained. In this case Lyapunov exponent vanishes. The results of the correlation analysis show that the autocorrelation function vanishes to zero faster than the exponent function for this dynamical mode. Such state can be called pseudochaotical. It was proved, that the intermittency in Hamiltonian maps appears in the alternative chaotization way. In contrast to the common processes of resonances destruction mechanism the new one is based on the property of the singular line to cut a phase space into unconnected parts. The new effective method for the transport acceleration under a stochastic force with a low amplitude in a dynamical chaos mode is suggested being especially effective for the intermittent systems. The method solves the targeting problem that allows to increase an efficiency of the all known methods of chaotic control.