title: Periodic perturbations of oscillators on the plane
metadata.name: dc.contributor.author
metadata.value: Bibikov, Yuri N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Vasil’eva, Ekaterina V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-05-30T15:01:49Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-05-30T15:01:49Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Bibikov Yu.N., Vasil’eva E.V. Periodic perturbations of oscillators on the plane. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2024, vol. 11 (69), issue 1, pp. 38–47. https://doi.org/10.21638/spbu01.2024.102 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2024.102
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/45449
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A review of the results of research carried out in the current century at the Department
  of Differential Equations of St. Petersburg State University is presented. We study the
  problem of stability of the zero solution of a second-order equation describing periodic perturbations
  of an oscillator with a nonlinear restoring force under reversible and conservative
  perturbations. Such perturbations are related to transcendental perturbations, in which, in
  order to solve the problem of stability, it is necessary to take into account all the terms of
  the expansion of the right side of the equation into a series. The problem of stability under
  transcendental perturbations was posed in 1893 by A. M. Lyapunov. The results presented
  in this article on the stability of the oscillator were carried out using the KAM-theory
  methods: perturbations of the oscillator with infinitely small and infinitely large oscillation
  frequencies are considered; conditions for the presence of quasi-periodic solutions in any
  neighborhood of the time axis are given, from which follows the stability (not asymptotic)
  of the zero solution of the perturbed equation; stability conditions are given for the zero
  solution of a Hamiltonian system with two degrees of freedom, the unperturbed part of
  which is described by a pair of oscillators (in this case, conservative perturbations are considered).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 11 (69); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: harmonic oscillator
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: KAM theory
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: conservative perturbations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: reversible perturbations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Hamiltonian system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quasi-periodic solutions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Periodic perturbations of oscillators on the plane
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 38-47.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/45449/1/38-47.pdf
resources.format: Adobe PDF
resources.size: 281,6 kB