On the effectiveness of Hamiltonian uniformly small and infinitesimal perturbations of linear Hamiltonian systems

It is proved that the set of all limiting values of solutions' arbitrary indicator of the linear Hamiltonian system under uniformly small perturbations for the linear Hamiltonian system is the same as the similar set obtained by uniformly small Hamiltonian perturbations. Also it is proved that the set of all values of solutions' arbitrary indicator of the linear Hamiltonian system under infinitesimal perturbations for the linear Hamiltonian system is the same as the similar set obtained by infinitesimal Hamiltonian perturbations.