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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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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