title: Two-dimensional homogeneous cubic systems: Classification and normal forms — VI
metadata.name: dc.contributor.author
metadata.value: Basov, Vladimir V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Chermnykh, Aleksandr S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-09-10T13:18:17Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-09-10T13:18:17Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Basov V. V., Chermnykh A. S. Two-dimensional homogeneous cubic systems: Classification and normal forms — VI. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 3, pp. 377–391.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.302
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/19389
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The present article is the sixth in a series of papers dedicated to two-dimensional cubic
  homogeneous systems. It considers a case when a homogeneous polynomial vector in the
  right-hand part of the system does not have a common factor. A set of such systems is
  divided into classes of linear equivalence, wherein the simplest system being a third-order
  normal form is distinguished on the basis of properly introduced principles. Such a form is
  defined by the matrix of its right-hand part coefficients, which is called the canonical form
  (CF). Each CF has its own arrangement of non-zero elements, their specific normalization
  and canonical set of permissible values for the unnormalized elements, which relates the CF
  to the selected class of equivalence. In addition to classification, each CF is provided with:
  a) conditions on the coefficients of the initial system, b) non-singular linear substitutions
  that reduce the right-hand part of the system under these conditions to the selected CF,
  c) obtained values of CF’s unnormalized elements. The proposed classification was primarily
  created to obtain all possible structures of generalized normal forms for systems with CF in
  the unperturbed part. The article presents another application of the resulting classification
  related to finding phase portraits in the Poincare circle for CF.
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 7 (65); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: homogeneous cubic system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: normal form
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: canonical form
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Two-dimensional homogeneous cubic systems: Classification and normal forms — VI
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 377-391.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/19389/1/377-391.pdf
resources.format: Adobe PDF
resources.size: 370,14 kB