title: Different types of stable periodic points of diffeomorphism of a plane with a homoclinic orbit
metadata.name: dc.contributor.author
metadata.value: Vasil’eva, Ekaterina V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-07-16T14:45:26Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-07-16T14:45:26Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vasil’eva E.V. Different types of stable periodic points of diffeomorphism of a plane with a homoclinic orbit. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 2, pp. 295–304.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.209
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/29884
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A diffeomorphism of the plane into itself with a fixed hyperbolic point is considered; the
  presence of a nontransverse homoclinic point is assumed. Stable and unstable manifolds
  touch each other at a homoclinic point; there are various ways of touching a stable and
  unstable manifold. In the works of Sh. Newhouse, L. P. Shilnikov and other authors, studied
  diffeomorphisms of the plane with a nontranverse homoclinic point, under the assumption
  that this point is a tangency point of finite order. It follows from the works of these authors
  that an infinite set of stable periodic points can lie in a neighborhood of a homoclinic point;
  the presence of such a set depends on the properties of the hyperbolic point. In this paper,
  it is assumed that a homoclinic point is not a point at which the tangency of a stable and
  unstable manifold is a tangency of finite order. Allocate a countable number of types of
  periodic points lying in the vicinity of a homoclinic point; points belonging to the same
  type are called n-pass (multi-pass), where n is a natural number. In the present paper,
  it is shown that if the tangency is not a tangency of finite order, the neighborhood of a
  nontransverse homolinic point can contain an infinite set of stable single-pass, double-pass,
  or three-pass periodic points with characteristic exponents separated from zero.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by Russian Foundation for Basic Research (grant no. 19-01-00388).
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 8 (66); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: diffeomorphism
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: nontransverse homoclinic point
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: characteristic exponents
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Different types of stable periodic points of diffeomorphism of a plane with a homoclinic orbit
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 295-304.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/29884/1/295-304.pdf
resources.format: Adobe PDF
resources.size: 305,38 kB