title: Multi-pass 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: 2021-10-07T11:44:19Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-10-07T11:44:19Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vasil’eva E.V. Multi-pass 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 3, pp. 406–416.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.303
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/33257
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A diffeomorphism of a plane into itself with a fixed hyperbolic point and a nontransversal
  point homoclinic to it is studied. There are various ways of touching a stable and unstable
  manifold at a homoclinic point. Periodic points whose trajectories do not leave the vicinity
  of the trajectory of a homoclinic point are divided into a countable set of types. Periodic
  points of the same type are called n-pass periodic points if their trajectories have n turns
  that lie outside a sufficiently small neighborhood of the hyperbolic point. Earlier in the
  articles of Sh. Newhouse, L. P. Shil’nikov, B. F. Ivanov and other authors, diffeomorphisms
  of the plane with a nontransversal homoclinic point were studied, it was assumed that this
  point is a tangency point of finite order. In these papers, it was shown that in a neighborhood
  of a homoclinic point there can be infinite sets of stable two-pass and three-pass
  periodic points. The presence of such sets depends on the properties of the hyperbolic point.
  In this paper, it is assumed that a homoclinic point is not a point with a finite order of
  tangency of a stable and unstable manifold. It is shown in the paper that for any fixed natural
  number n, a neighborhood of a nontransversal homolinic point can contain an infinite
  set of stable n-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 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: diffeomorphism of plane
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: nontransversal 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: Multi-pass 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: 406-416.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/33257/1/406-416.pdf
resources.format: Adobe PDF
resources.size: 313,04 kB