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

Abstract

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.