The estimate of accuracy of the rational approximation of the monodromy operator

The paper deals with the problem of investigation of eigenvalues of the monodromy operator for periodic solutions of nonlinear delay-differential equations. In the case the period of the solution is not commensurate with the delay time, the rational approximation is used. Thus the eigenvalues depend on the perturbation parameter. In this paper, a similar problem for a nonlinear system of ordinary differential equations is considered. Necessary and sufficient conditions for the Lipschitz behaviour of the eigenvalues are obtained.