Phase trajectory analysis at the nonlinear resonances

The phase trajectories close to the parametric resonance and to the nonlinear resonances of third and fourth order, which play an important role in cyclic accelerator particle dynamics, are investigated. The problem is reduced to the construction of phase trajectories that are third- or fourth-order curves and the determination of the mode of motion in the vicinity of the resonance. The phase trajectory build-up is performed using Klein´s perturbation method.<>