Naplekov D. Reflection processes in systems with nonsmooth boundaries.

The thesis is devoted to a study of the processes and search of a new effects occurring with reflections or collisions in nonlinear systems with complex boundary. Simple model that implements Fermi acceleration and allows for accurate description is considered. For this system the existence of trajectories, on which particles gain unlimited energy was shown. Absence of energy limit proved analytically. The model of diffusely reflecting surface on the basis of open billiard is proposed. Its indicatrix of reflection coincides with the model Lambert indicatix in case of strongly chaotic billiards. The method of construction of an open billiard with mirror-diffuse indicatrix of reflection is proposed. Billiards are built with this dependence coinciding with the experimentally observed ones, it is shown that the diffuse part of their indicatrix differs from the model one and qualitatively coincides with the experimentally observed indicatrixes. Also considered is collisionless ideal gas in the connected ergodic and not ergodic vessels. It is shown that in the equation of state of the gas in first vessel appears associated with nonergodicity amendment to the vessel's volume It is shown that this amendment well correlates with the share of the phase space under remaining islands of stability.