Prof. Dr. Anatoly Neyshtadt,Space Research Institute of Russian Academy of Sciences, Russia and Department of Mathematical Sciences, Loughborough University, UK

2015.4.10 10:00-11:00am Z311

Small perturbations imposed on an integrable nonlinear oscillatory system cause a slow evolution of values that were integrals of the unperturbed system. According to the classical averaging method, for an approximate description of this evolution one should average the speed of evolution over all the phases of the unperturbed oscillations. This simple recipe does not always produce correct results due to resonances arising in the process of evolution. The phenomenon of capture into resonance consists in the system starting to evolve in such a way as to preserve the resonance property once it has arisen. When passing through the resonance without capture, the phase trajectories somewhat deviate in a quasi-random manner from the motion predicted by the averaging method. This phenomenon is called a scattering on a resonance. In the talk, a general theory of passages through resonances and captures into resonance, as well as several examples of these phenomena in dynamics of charged particles will be presented.