title: Stable periodic solutions of periodic systems of differential equations
metadata.name: dc.contributor.author
metadata.value: Vasil’eva, Ekaterina V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-04-26T09:15:59Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-04-26T09:15:59Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vasil’eva E.V. Stable periodic solutions of periodic systems of differential equations. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 1, pp. 14– 21.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.102
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9494
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: An infinitely differentiable periodic two-dimensional system of differential equations is
  considered. It is assumed that there is a hyperbolic periodic solution, as well as the presence
  of a homoclinic solution to the periodic solution. It follows from the works of Sh. Newhouse,
  L. P. Shil’nikov, B. F. Ivanov and others that under certain conditions a neighborhood of the
  non-transversal homoclinic solution contains a countable set of stable periodic solutions,
  but at least one of the characteristic exponents in these solutions tends to zero with
  increasing period. Earlier, in the author’s work a two-dimensional diffeomorphism was
  considered and it was shown that for a certain type of tangency of the stable and unstable
  manifolds, a neighborhood homoclinic point contains a countable set of stable periodic points
  with characteristic exponents bounded away from zero. The aim of the present paper is
  to distinguish a class of two-dimensional periodic systems of differential equations which
  Poincare transformation is a diffeomorphism that has an infinite set of stable periodic points
  in the neighborhood of a nontransversal homoclinic point. It is shown that for a certain
  method of tangency of a stable and unstable manifolds an arbitrary neighborhood of a
  nontransversal homoclinic solution contains a countable set of stable periodic solutions.
  Characteristic exponents of these solutions are separated from zero.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при частичной финансовой поддержке РФФИ (грант №16-01-00452).
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 5(63); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: nontransversal homoclinic solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: characteristic exponent
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stable periodic solutions of periodic systems of differential equations
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 02-Vasileva.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9494/1/02-Vasileva.pdf
resources.format: Adobe PDF
resources.size: 285,18 kB