Abstract: The particle nonlinear motion equation for a radial sector cyclotron with N-folded symmetry was derived. The betalron oscillations frequency with N = 4. 5, 6, 8, 10 and the phase planar properlies before and after v_y= 4/3 resonance with N= 4, f=0.578 were analyzed, by using numerical method. The dynamic stabililies and nonlinear properties were discussed, the result compared with those of ref. [1] shows that both are consistent when nonlinear terms are neglected.

Key words: symplectic matrix, QR-like algorithm, eigenvalue, condition number, Jordan canonical form, Schur canonical form