SYMPLECTIC MATRICES AND STRONG STABILITY OF HAMILTONIAN SYSTEMS WITH PERIODIC COEFFICIENTS

A theory of the analysis of strong stability of Hamiltonian systems with periodic coefficients is presented. It is based on the strong stability of fundamental solution evaluated at its period. However, the matrix solution being symplectic, this analysis leads to the search of strong stability of a symplectic matrix. A method for the determination of the monodromy matrix is given and an application of this study on two Hamiltonian systems with periodic coefficients from the book of Yakubovich and Starzhinskii, is presented.