This article is cited in 5 scientific papers (total in 5 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
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.
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Mathematics of the USSR-Sbornik, 1974, 23:3, 382–404
MSC: Primary 34C35, 34C20; Secondary 34D20
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
\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.)
\jour Math. USSR-Sb.
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T. Krüger, L. D. Pustyl'nikov, S. Troubetzkoy, “The nonautonomous function-theoretic center problem”, Bol Soc Bras Mat, 30:1 (1999), 1
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
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
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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