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Decaying Oscillatory Perturbations of Hamiltonian Systems in the Plane. / Sultanov, O. A.

In: Journal of Mathematical Sciences (United States), Vol. 257, No. 5, 01.09.2021, p. 705-719.

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Sultanov, OA 2021, 'Decaying Oscillatory Perturbations of Hamiltonian Systems in the Plane', Journal of Mathematical Sciences (United States), vol. 257, no. 5, pp. 705-719. https://doi.org/10.1007/s10958-021-05511-2

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Sultanov, O. A. / Decaying Oscillatory Perturbations of Hamiltonian Systems in the Plane. In: Journal of Mathematical Sciences (United States). 2021 ; Vol. 257, No. 5. pp. 705-719.

BibTeX

@article{54e7f6da0ea4437fbcd1f4dcbfa380a9,
title = "Decaying Oscillatory Perturbations of Hamiltonian Systems in the Plane",
abstract = "We study the influence of decaying perturbations on autonomous oscillatory systems in a plane under the assumption that the perturbations preserve the equilibrium state of the limit system, oscillate with asymptotically constant frequency, and satisfy the nonresonance condition. We discuss the long-term behavior of the perturbed trajectories in a neighborhood of the equilibrium state. We describe conditions on the perturbation parameters that guarantee preservation or loss of stability of the equilibrium. The results are illustrated by an example of decaying perturbations of the Duffing oscillator.",
author = "Sultanov, {O. A.}",
year = "2021",
month = sep,
day = "1",
doi = "10.1007/s10958-021-05511-2",
language = "English",
volume = "257",
pages = "705--719",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "5",

}

RIS

TY - JOUR

T1 - Decaying Oscillatory Perturbations of Hamiltonian Systems in the Plane

AU - Sultanov, O. A.

PY - 2021/9/1

Y1 - 2021/9/1

N2 - We study the influence of decaying perturbations on autonomous oscillatory systems in a plane under the assumption that the perturbations preserve the equilibrium state of the limit system, oscillate with asymptotically constant frequency, and satisfy the nonresonance condition. We discuss the long-term behavior of the perturbed trajectories in a neighborhood of the equilibrium state. We describe conditions on the perturbation parameters that guarantee preservation or loss of stability of the equilibrium. The results are illustrated by an example of decaying perturbations of the Duffing oscillator.

AB - We study the influence of decaying perturbations on autonomous oscillatory systems in a plane under the assumption that the perturbations preserve the equilibrium state of the limit system, oscillate with asymptotically constant frequency, and satisfy the nonresonance condition. We discuss the long-term behavior of the perturbed trajectories in a neighborhood of the equilibrium state. We describe conditions on the perturbation parameters that guarantee preservation or loss of stability of the equilibrium. The results are illustrated by an example of decaying perturbations of the Duffing oscillator.

UR - http://www.scopus.com/inward/record.url?scp=85113887570&partnerID=8YFLogxK

U2 - 10.1007/s10958-021-05511-2

DO - 10.1007/s10958-021-05511-2

M3 - Article

AN - SCOPUS:85113887570

VL - 257

SP - 705

EP - 719

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 126272610