title: Stable and completely unstable periodic points of diffeomorphism of a plane with a heteroclinic contour
metadata.name: dc.contributor.author
metadata.value: Vasil’eva, Ekaterina V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-09-10T13:24:31Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-09-10T13:24:31Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vasil’eva E. V. Stable and completely unstable periodic points of diffeomorphism of a plane with a heteroclinic contour. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 3, pp. 392–403.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.303
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/19390
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We study the diffeomorphism of a plane into itself with three fixed hyperbolic points. It
  is assumed that at the intersections of the unstable manifold of the first point and the
  stable manifold of the second point, the unstable manifold of the second point and the
  stable manifold of the third point, the unstable manifold of the third first point and the
  stable manifold of the first point are heteroclinic points. The orbits of fixed and heteroclinic
  points form a heteroclinic contour. The case is studied when stable and unstable manifolds
  intersect non-transversally at heteroclinic points. Among the points of non-transversal intersection of a stable manifold with an unstable manifold, first of all, points of tangency of
  finite order are distinguished; in this paper, such points are not considered. In the works
  of L. P. Shilnikov, S. V. Gonchenko and other authors studied diffeomorphism with heteroclinic contour, it was assumed that the points of non-transversal intersection of a stable and unstable manifolds are points of tangency of finite order. It follows from the works of
  these authors that there exist diffeomorphisms for which there are stable and completely
  unstable periodic points in the neighborhood of the heteroclinic contour. In this paper, it
  is assumed that the points of a non-transversal intersection of a stable and unstable manifolds are not points of tangency of finite order. It is shown that in the neighborhood of
  such a heteroclinic contour two countable sets of periodic points can lie. One of these sets
  consists of stable periodic points, whose characteristic exponents are separated from zero,
  the second — from completely unstable periodic points, whose characteristic exponents are
  also 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 7 (65); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: diffeomorphism of plane
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: hyperbolic fixed points
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: heteroclinic points
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: heteroclinic contour
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: non-transversal intersection
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stability
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stable and completely unstable periodic points of diffeomorphism of a plane with a heteroclinic contour
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 392-403.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/19390/1/392-403.pdf
resources.format: Adobe PDF
resources.size: 309,32 kB