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We consider the hamiltonian system of linear differential equations with periodic coefficients. Using the infinite determinant method based on the existence of periodic solutions on the boundaries between the domains of stability and instability in the parameter space we have developed the algorithm for analytical computation of the stability boundaries. The algorithm has been realized for the second and the fourth order hamiltonian systems arising in the restricted many-body problems. Thedoi:10.3846/13926292.2005.9637281 fatcat:ciyc52odpnhpbdu3ydb4m6qbxy