Geodesic
Stable and oscillating motions in nonautonomous dynamical systems. A generalization of C. L. Siegel's theorem to the nonautonomous case
Sbornik. Mathematics, Tome 23 (1974) no. 3, pp. 382-404 
L. D. Pustyl'nikov. Stable and oscillating motions in nonautonomous dynamical systems. A generalization of C. L. Siegel's theorem to the nonautonomous case. Sbornik. Mathematics, Tome 23 (1974) no. 3, pp. 382-404. http://geodesic.mathdoc.fr/item/SM_1974_23_3_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we generalize to the nonautonomous case a theorem of C. L. Siegel on the reducibility of an analytic dynamical system to normal form in a neighborhood of an equilibrium point. In fact, under certain concrete assumptions with respect to the behavior of the system as $t\to\infty$, we show that in a neighborhood of an equilibrium we can reduce the system to a linear system by means of a change of coordinates that depends on the time $t$ and is analytic in the remaining variables. The results obtained are applicable to the problem of the stability of an equilibrium point. Bibliography: 16 titles.

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[10] A. D. Bryuno, “Analiticheskaya forma differentsialnykh uravnenii”, Trudy Mosk. matem. ob-va, XXV (1971), 119–202

[11] A. D. Bryuno, “O lokalnykh invariantakh differentsialnykh uravnenii”, Matem. zametki, 14:4 (1973), 499–507 | Zbl

[12] Yu. N. Bibikov, “O suschestvovanii uslovno-periodicheskikh reshenii sistem differentsialnykh uravnenii”, Diff. ur., VII:8 (1971), 1347–1356 | MR

[13] Yu. N. Bibikov, “O privodimosti sistemy dvukh differentsialnykh uravnenii k normalnoi forme”, Diff. ur., VII:10 (1971), 1899–1902 | MR

[14] L. D. Pustylnikov, “Obobschenie dvukh teorem K. L. Zigelya na neavtonomnyi sluchai”, Uspekhi matem. nauk, XXVI:4 (160) (1971), 247–248 | MR

[15] L. D. Pustylnikov, “Ob ustoichivosti polutraekterii pri otobrazhenii ploskosti, sokhranyayuschem ploschad”, DAN SSSR, 202:1 (1972), 38–40 | MR

[16] L. D. Pustylnikov, “Suschestvovanie mnozhestva polozhitelnoi mery ostsilliruyuschikh dvizhenii v odnoi zadache dinamiki”, DAN SSSR, 202:2 (1972), 287–289 | MR