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

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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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     author = {L. D. Pustyl'nikov},
     title = {Stable and oscillating motions in nonautonomous dynamical systems. {A~generalization} of {C.\,L.~Siegel's} theorem to the nonautonomous case},
     journal = {Sbornik. Mathematics},
     pages = {382--404},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_23_3_a3/}
}
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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/