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 Mat. Sb. (N.S.), 1974, Volume 94(136), Number 3(7), Pages 407–429 (Mi msb3689)

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.

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English version:
Mathematics of the USSR-Sbornik, 1974, 23:3, 382–404

Bibliographic databases:

UDC: 517.9
MSC: Primary 34C35, 34C20; Secondary 34D20

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”, Mat. Sb. (N.S.), 94(136):3(7) (1974), 407–429; Math. USSR-Sb., 23:3 (1974), 382–404

Citation in format AMSBIB
\Bibitem{Pus74} \by L.~D.~Pustyl'nikov \paper Stable and oscillating motions in nonautonomous dynamical systems. A~generalization of C.\,L.~Siegel's theorem to the nonautonomous case \jour Mat. Sb. (N.S.) \yr 1974 \vol 94(136) \issue 3(7) \pages 407--429 \mathnet{http://mi.mathnet.ru/msb3689} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=364764} \zmath{https://zbmath.org/?q=an:0321.34043} \transl \jour Math. USSR-Sb. \yr 1974 \vol 23 \issue 3 \pages 382--404 \crossref{https://doi.org/10.1070/SM1974v023n03ABEH001723} 

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This publication is cited in the following articles:
1. L. D. Pustyl'nikov, “Poincaré models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism”, Russian Math. Surveys, 50:1 (1995), 145–189
2. T. Krüger, L. D. Pustyl'nikov, S. Troubetzkoy, “The nonautonomous function-theoretic center problem”, Bol Soc Bras Mat, 30:1 (1999), 1
3. Alessandro Fortunati, Stephen Wiggins, “A Kolmogorov Theorem for Nearly Integrable Poisson Systems with Asymptotically Decaying Time-dependent Perturbation”, Regul. Chaotic Dyn., 20:4 (2015), 476–485
4. Rafael de la Llave, “Simple Proofs and Extensions of a Result of L. D. Pustylnikov on the Nonautonomous Siegel Theorem”, Regul. Chaotic Dyn., 22:6 (2017), 650–676
5. Rafael de la Llave, “Uniform Boundedness of Iterates of Analytic Mappings Implies Linearization: a Simple Proof and Extensions”, Regul. Chaotic Dyn., 23:1 (2018), 1–11
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