Probability phenomena in perturbed dynamical systems

Main page



If in a deterministic dynamical system a small variation of initial conditions produces a significant change of motion, then the behavior of such a system is practically non-distinguishable from a random one. This non-rigorous assertion lies in the foundation of the deterministic chaos theory. Such quasi-random behavior exists also in systems which differ by an arbitrary small perturbation from systems with a very simple (periodic or quasi-periodic) dynamics. Different kinds of perturbed motion have certain probabilities, and analysis of dynamics on long time intervals leads to random walk problems. The theory of this behavior describes various phenomena lice captures of satellites into a resonance, surfatron acceleration of charged particles, streamline chaos in stationary flows.