title: Generalized normal forms of the systems of ordinary differential equations with a quasi-homogeneous polynomial (αx21 + x2, x1x2) in the unperturbed part
metadata.name: dc.contributor.author
metadata.value: Basov, Vladimir V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Zefirov, Artem V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-05-04T18:48:13Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-05-04T18:48:13Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Basov V.V., Zefirov A.V. Generalized normal forms of the systems of ordinary differential equations with a quasi-homogeneous polynomial (αx21 + x2, x1x2) in the unperturbed part. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 1, pp. 12–28.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.102
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/28430
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper a study on constructive construction of the generalized normal forms (GNF)
  is continued. The planar real-analytical at the origin system is considered. Its unperturbed
  part forms a first degree quasi-homogeneous first degree polynomial (αx21
  + x2, x1x2) of
  type (1, 2) where parameter α ∈  2 (−1/2, 0)[(0, 1/2]. For given value of   this polynomial is
  a canonical form, that is an element of a class of equivalence relative to quasi-homogeneous
  substitutions of zero order into which any first order quasi-homogeneous polynomial of type
  (1, 2) is divided in accordance with the chosen structural principles due to it only making
  sense to reduce the systems with the various canonical forms in their unperturbed part to
  GNF. Based on the constructive method of resonance equations and sets, the resonance
  equations are derived. Perturbations of the acquired system satisfies these equations if
  an almost identity quasi-homogeneous substitution in the given system is applied. Their
  validity guarantees formal equivalence of the systems. Besides, resonance sets of coefficients
  are specified that allows to get all possible GNF structures and prove reducibility of the
  given system to a GNF with any of specified structures. In addition, some examples of
  characteristic GNFs are provided including that with the parameter   leading to appearance
  of an additional resonance equation and the second nonzero coefficient of the appropriate
  orders in GNFs.
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 8 (66); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: generalized normal form
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quasi-homogeneous polynomial
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: resonance equation
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Generalized normal forms of the systems of ordinary differential equations with a quasi-homogeneous polynomial (αx21 + x2, x1x2) in the unperturbed part
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 12-28.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/28430/1/12-28.pdf
resources.format: Adobe PDF
resources.size: 365,11 kB