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

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On the Stability of the Nonlinear Center under Quasi-periodic Perturbations. / Basov, V. V.; Bibikov, Yu N.

In: Vestnik St. Petersburg University: Mathematics, Vol. 53, No. 2, 01.04.2020, p. 174-179.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{53c0211d2aef487f9da03d7f8f16f026,

title = "On the Stability of the Nonlinear Center under Quasi-periodic Perturbations",

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 (x) triple over dot + x(2n-1) = 0, n is an integer number, n >= 2, under {"}small{"} quasi-periodic perturbations.",

keywords = "center, quasi-periodic function, stability",

author = "Basov, {V. V.} and Bibikov, {Yu N.}",

year = "2020",

month = apr,

day = "1",

doi = "10.1134/S1063454120020041",

language = "English",

volume = "53",

pages = "174--179",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - On the Stability of the Nonlinear Center under Quasi-periodic Perturbations

AU - Basov, V. V.

AU - Bibikov, Yu N.

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