Vavilov State Optical Institute^1, ITMO University^2, Russia

In a dynamical billiard – traps or cavities – the periodic oscillations of their walls or mirrors result in energy exchange between walls and objects inside the trap. In the talk, presented and compared are general features of temporal and spatial structures formed by classical and quantum particles, waves, and solitons in dynamical billiards. Considered is the dynamics of classical particles in one-dimensional geometry of dynamical billiard, (quasienergy) states of a single quantum particle in a potential well with periodically oscillating wells and decay of these states in “non-ideal” traps, and nonlinear structures, including nonlinear Rabi oscillations and “longitudinal” and “transverse” solitons of Bose-Einstein condensates.