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

Dosso Mouhamadou, Traore G. Y. Arouna, Jean-Claude Koua Brou

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.

 

Keywords

Symplectic matrices, Isotropic subspaces, Hamiltonian systems, Fundamental solutions, rang-k perturbation, Stability(strong), Mathieu systems

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