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On the Stability of the Nonlinear Center under Quasi-periodic Perturbations. / Basov, V. V.; Bibikov, Yu N.
в: Vestnik St. Petersburg University: Mathematics, Том 53, № 2, 01.04.2020, стр. 174-179.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On the Stability of the Nonlinear Center under Quasi-periodic Perturbations
AU - Basov, V. V.
AU - Bibikov, Yu N.
N1 - Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - 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 (x) triple over dot + x(2n-1) = 0, n is an integer number, n >= 2, under "small" quasi-periodic perturbations.
AB - 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 (x) triple over dot + x(2n-1) = 0, n is an integer number, n >= 2, under "small" quasi-periodic perturbations.
KW - center
KW - quasi-periodic function
KW - stability
UR - http://www.scopus.com/inward/record.url?scp=85085705047&partnerID=8YFLogxK
U2 - 10.1134/S1063454120020041
DO - 10.1134/S1063454120020041
M3 - Article
AN - SCOPUS:85085705047
VL - 53
SP - 174
EP - 179
JO - Vestnik St. Petersburg University: Mathematics
JF - Vestnik St. Petersburg University: Mathematics
SN - 1063-4541
IS - 2
ER -
ID: 70963548