title: On finding generalized normal forms of systems with a Hamiltonian unperturbed part using the Belitskii method
metadata.name: dc.contributor.author
metadata.value: Vaganyan, Artur S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-09-28T15:31:55Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-09-28T15:31:55Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vaganyan A. S. On finding generalized normal forms of systems with a Hamiltonian unperturbed part using the Belitskii method. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 3, pp. 372–376.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2016.303
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/3905
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This work continues an article written in collaboration with V. V. Basov about finding the structures
  of generalized normal forms of two-dimensional autonomous systems of ordinary differential equations
  with a Hamiltonian unperturbed part and non-Hamiltonian perturbation. In this article we consider the
  case of systems of four and more equations with a Hamiltonian quasi-homogeneous unperturbed part
  generated by the Hamiltonian of the form H =  n
  i=1 Hi(xi, yi). By means of a special decomposition of
  the perturbation similar to splitting into Hamiltonian and non-Hamiltonian components that was used by
  A. Baider and J. Sanders in two-dimensional case, we reduce the problem of finding the generalized normal
  form for such a system to the question about the normal form of power series. Normalization of a power
  series was studied earlier by G. R. Belitskii. We use the method of G. R. Belitskii and develop his ideas by
  introducing the notions of Hamiltonian resonant and reduced resonant sets, and in these terms formulate
  the normalization theorem. As a consequence of the theorem we give a generalization of the result due to Takens on the normal form of a system with a nilpotent linear part to the case of an arbitrary number of
  Jordan blocks. In particular, for n = 2 we find explicitly one of the generalized normal forms in the sense
  of V. V. Basov for a system of four equations with an unperturbed part (y1, 0, y2, 0). Refs 7.
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. Series 1. Mathematics. Mechanics. Astronomy;Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: normal forms
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Belitskii method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Takens normal form
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On finding generalized normal forms of systems with a Hamiltonian unperturbed part using the Belitskii method
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Vaganyan.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/3905/1/Vaganyan.pdf
resources.format: Adobe PDF
resources.size: 206,91 kB