Resonances in Four-Dimensional Quasi-Hamiltonian Systems: Analysis and Simulations

The problem of qualitative behaviour of four-dimensional quasi-Hamiltonian system in a neighbourhood of a fixed resonance is considered. The general analytical grounds of the problem are touched upon. We turn to the global analysis of special three-dimensional system averaged near the resonance. Furthermore, a checking the theory against numerical simulations is made. Two physical examples, revealing an irregular resonant dynamics, are studied.