Rank-k perturbation of Hamiltonian Systems with Periodic Coefficients and Applications
DOI:
https://doi.org/10.29020/nybg.ejpam.v12i4.3574Keywords:
Symplectic matrices, Isotropic subspaces, Hamiltonian systems, Fundamental solutions, rang-k perturbation, Stability(strong), Mathieu systemsAbstract
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.
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