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Motion of charged particle in given fields in a cyclic accelerator has been investigated. The nonlinear problem of finding stable trajectories in the vicinity of a resonance has been solved. The equations of motion for charged particle deviation from ideal orbit or the betatron oscillations equations (which are lateral to the closed orbit oscillations with the frequencies UZ, VZ) [I] are the equations:

The betatron oscillations in the vicinity of nonlinear resonance in cyclic accelerator investigation