Geodesic
Resonance in multicomponent linear systems
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2021), pp. 74-79

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We consider large systems of point particles with arbitrary quadratic interaction and harmonic force acting on one fixed particle. Necessary and sufficient conditions for resonance and for uniform boundedness of trajectories are obtained. In the case of resonance, we obtained the large time asymptotics for energy maxima. 
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     title = {Resonance in multicomponent linear systems},
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A. A. Lykov; V. A. Malyshev; M. V. Melikian. Resonance in multicomponent linear systems. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2021), pp. 74-79. http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a11/