Geodesic
Proof of simultaneous conditional exponential stabilization and destabilization of linear Hamiltonian systems
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2018), pp. 65-68

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It is proved that any linear Hamiltonian system is simultaneously conditionally (with respect to a subspace of half dimension) exponentially stabilizable and destabilizable by uniformly small Hamiltonian perturbations. 
@article{VMUMM_2018_4_a12,
     author = {T. V. Salova},
     title = {Proof of simultaneous conditional exponential stabilization and destabilization of linear {Hamiltonian} systems},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {65--68},
     publisher = {mathdoc},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_4_a12/}
}
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T. V. Salova. Proof of simultaneous conditional exponential stabilization and destabilization of linear Hamiltonian systems. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2018), pp. 65-68. http://geodesic.mathdoc.fr/item/VMUMM_2018_4_a12/