Abstract
The problem of stability of the zero solution of a system with a “center”-type critical point at the origin of coordinates is considered. For the first time, such a problem for autonomous systems was investigated by A.M. Lyapunov. We continued Lyapunov’s investigations for systems with a periodic dependence on time. In this paper, systems with a quasi-periodic time dependence are considered. It is assumed that the basic frequencies of quasi-periodic functions satisfy the standard Diophantine-type condition. The problem under consideration can be interpreted as the problem of stability of the state of equilibrium of the oscillator \(\ddot {x} + {{x}^{{2n - 1}}}\) = 0, n is an integer number, n ≥ 2, under “small” quasi-periodic perturbations.
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REFERENCES
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In memory of V.A. Pliss
Translated by E. Smirnova
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Basov, V.V., Bibikov, Y.N. On the Stability of the Nonlinear Center under Quasi-periodic Perturbations. Vestnik St.Petersb. Univ.Math. 53, 174–179 (2020). https://doi.org/10.1134/S1063454120020041
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DOI: https://doi.org/10.1134/S1063454120020041