Geodesic
The proof of simultaneous conditional stabilization and destabilization of linear Hamiltonian systems
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2017), pp. 8-15

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It is proved that each linear Hamiltonian system is simultaneously conditionally (with respect to a subspace of half dimension) stabilizable and destabilizable by infinitesimal Hamiltonian perturbation. 
@article{VMUMM_2017_6_a1,
     author = {T. V. Salova},
     title = {The proof of simultaneous conditional stabilization and destabilization of linear {Hamiltonian} systems},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {8--15},
     publisher = {mathdoc},
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     year = {2017},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2017_6_a1/}
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T. V. Salova. The proof of simultaneous conditional stabilization and destabilization of linear Hamiltonian systems. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2017), pp. 8-15. http://geodesic.mathdoc.fr/item/VMUMM_2017_6_a1/