Approximation of eigenvalues of evolution operators for linear retarded functional differential equations (Q2903045)

The authors consider for the linear retarded functional differential equation NEWLINE\[NEWLINEy'(t)=f(t,y_t), \, t\in INEWLINE\]NEWLINE the reduction to finite dimension of the relevant evolution operators by a pseudospectral collocation and study how the nonzero eigenvalues of such operators are approximated by the eigenvalues of their finite-dimensional versions. The most relevant applications such as the determination of the asymptotic stability of equilibria and periodic solutions of nonlinear autonomous retarded functional differential equations are also discussed. Numerical tests are provided.