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arXiv · 1712.03604

On a perturbation theory of Hamiltonian systems with periodic coefficients

Traoré G. Y. Arouna·Mouhamadou Dosso·Jean-Claude Koua Brou
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Abstract

A theory of rank $k\ge 2$ perturbation of symplectic matrices and Hamiltonian systems with periodic coefficients using a base of isotropic subspaces, is presented. After showing that the fundamental matrix ${\displaystyle \left(\widetilde{X}(t)\right)_{t\ge 0}}$ of the rank $k$ perturbation of Hamiltonian system with periodic coefficients and the rank $k$ perturbation of the fundamental matrix ${\displaystyle \left(X(t)\right)_{t\ge 0}}$ of the unperturbed system are the same, the Jordan canonical form of ${\displaystyle \left(\widetilde{X}(t)\right)_{t\ge 0}}$ is given. Two numerical examples illustrating this theory and the consequences of rank $k$ perturbations on the strong stability of Hamiltonian systems were also given.

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Traoré G. Y. Arouna, Mouhamadou Dosso, Jean-Claude Koua Brou. 2017-12-10. On a perturbation theory of Hamiltonian systems with periodic coefficients. https://arxiv.org/abs/1712.03604

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