title: Invariant surfaces of periodic systems with conservative cubic first approximation
metadata.name: dc.contributor.author
metadata.value: Basov, Vladimir V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Zhukov, Artem S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-09-05T15:14:27Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-09-05T15:14:27Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Basov V.V., Zhukov A. S. Invariant surfaces of periodic systems with conservative cubic first approximation. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 3, pp. 376–393.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.303
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16314
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We study simultaneously two classes of time periodic systems of ODEs with small parameter "   0 : systems with “fast” and “slow” time. Their corresponding unperturbed systems x˙ i = − iyi"  , y˙i = i(x3 i −  ixi)"  (i = 1, n,   = 0, 1) have from one to 3n equilibrium points. We give explicit conditions on perturbations independent from parameter, which in both cases guarantee the existence of a certain number of invariant (n + 1)-dimensional surfaces, which are homeomorphic to tori for all sufficiently small values of the parameter. We provide explicit formulae of these surfaces, their asymptotic expansions and collections of systems with six invariant surfaces.
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 6 (64); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: invariant surface
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: bifurcation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: averaging
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: separatrix
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Invariant surfaces of periodic systems with conservative cubic first approximation
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 376-393.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16314/1/376-393.pdf
resources.format: Adobe PDF
resources.size: 440,68 kB