title: Stability of periodic solutions of periodic systems of differential equations with a heteroclinic contour
metadata.name: dc.contributor.author
metadata.value: Vasil’eva, Ekaterina V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-05-28T17:39:01Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-05-28T17:39:01Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vasil’eva E.V. Stability of periodic solutions of periodic systems of differential equations with a heteroclinic contour. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 2, pp. 297–308.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.212
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17944
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A two-dimensional periodic system of differential equations with two hyperbolic periodic
  solutions is considered, it is assumed that heteroclinic solutions lie at the intersection of
  stable and unstable manifolds of fixed points, more precisely, the existence of a heteroclinic
  contour is assumed. We study the case when stable and unstable manifolds intersect nontransversally
  at points of at least one heteroclinic solution. There are various ways of nontransversally
  intersecting a stable manifold with an unstable manifold at the points of a
  heteroclinic solution. Earlier in the works of L. P. Shil’nikov, S. V.Gonchenko, B. F. Ivanov
  and other authors, it was assumed that at the points of non-transversal intersection of a
  stable and unstable manifold there is a tangency of no more than finite order. It follows
  from the works of these authors that there exist systems in which there are stable periodic
  solutions in the neighborhood of the heteroclinic contour. In this paper, heteroclinic contours
  are studied under the assumption that at the points of non-transversal intersection of
  the stable and unstable manifold at the points of the heteroclinic solution, tangency is not a
  tangency of finite order. It is shown that in the neighborhood of such a heteroclinic contour
  there is situated a countable set of periodic solutions whose characteristic exponents are
  separated from zero.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported in part by Russian Foundation for Basic Research (grant N19-01-00388).
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 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: periodic systems of differential equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: hyperbolic solutions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: heteroclinic solutions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: nontransversal intersection
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stability
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stability of periodic solutions of periodic systems of differential equations with a heteroclinic contour
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 297-308.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17944/1/297-308.pdf
resources.format: Adobe PDF
resources.size: 314,94 kB