On the Stability of the Nonlinear Center under Quasi-periodic Perturbations

Результат исследований: Научные публикации в периодических изданияхстатья

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Аннотация

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 (Formula Presented.), n is an integer number, n ≥ 2, under “small” quasi-periodic perturbations.

Язык оригиналаанглийский
Страницы (с-по)174-179
Число страниц6
ЖурналVestnik St. Petersburg University: Mathematics
Том53
Номер выпуска2
DOI
СостояниеОпубликовано - 1 апр 2020

Предметные области Scopus

  • Математика (все)

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