Rank-k perturbation of Hamiltonian Systems with Periodic Coefficients and Applications

Jordan canonical forms of a rank-k perturbation of symplectic matrices and the fundamental solutions of Hamiltonian systems are presented on the basis of work done by C. Mehl et, al.. Small rank-k perturbations of Mathieu systems are analyzed. More precisely, it is shown that the rank-k perturbations of coupled or non-coupled double pendulums and the motion of an ion through a quadrupole analyzer slightly perturb the behavior of their spectra and their stabilities.