Geodesic
Oscillation and wandering of solutions to a second order differential equation
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2011), pp. 21-26

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The Lyapunov's oscillation and wandering characteristics of solutions to a second order linear equation are defined, namely, the mean frequency of a solution, of its derivative or their various linear combinations, the mean angular velocity of the vector composed of a solution and its derivative, also wandering indices derived from that velocity. Nearly all of the values introduced for any equation are proved to be the same: for the autonomic equation – just all (moreover they coincide with the modules of the imaginary parts of the roots of the characteristic polynomial), but even for the periodic one – generally speaking, not all. 
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     author = {I. N. Sergeev},
     title = {Oscillation and wandering of solutions to a second order differential equation},
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I. N. Sergeev. Oscillation and wandering of solutions to a second order differential equation. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2011), pp. 21-26. http://geodesic.mathdoc.fr/item/VMUMM_2011_6_a4/