Perturbations of Mathieu equations with parametric excitation of large period

We consider a linear differential system of Mathieu equations with periodic coefficients over periodic closed orbits and we prove that, arbitrarily close to this system, there is a linear differential system of Hamiltonian damped Mathieu equations with periodic coefficients over periodic closed orbits such that, all but a finite number of closed periodic coefficients, have unstable solutions. The perturbations will be peformed in the periodic coefficients.

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