|
This article is cited in 14 scientific papers (total in 14 papers)
Stable and oscillating motions in nonautonomous dynamical systems. A generalization of C. L. Siegel's theorem to the nonautonomous case
L. D. Pustyl'nikov
Abstract:
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.
Received: 21.06.1973
Citation:
L. D. Pustyl'nikov, “Stable and oscillating motions in nonautonomous dynamical systems. A generalization of C. L. Siegel's theorem to the nonautonomous case”, Math. USSR-Sb., 23:3 (1974), 382–404
Linking options:
https://www.mathnet.ru/eng/sm3689https://doi.org/10.1070/SM1974v023n03ABEH001723 https://www.mathnet.ru/eng/sm/v136/i3/p407
|
|