title: To the question of stability of periodic points of three-dimensional diffeomorphisms
metadata.name: dc.contributor.author
metadata.value: Vasilieva, Ekaterina V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-07-18T16:25:18Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-07-18T16:25:18Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vasilieva E.V. To the question of stability of periodic points of three-dimensional diffeomorphisms. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 2, pp. 193– 200.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.202
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/6941
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We consider diffeomorphism of three-dimensional space with a hyperbolic fixed point at the origin and
  nontransversal homoclinic point to it. It is follows from the works of Sh. Newhouse, L. P. Shil’nikov,
  B. F. Ivanov and others that under certain conditions a neighborhood of the homoclinic point contains a
  countable set of stable periodic points, but at least one of the characteristic exponents at these points
  tends to zero with increasing period. Earlier, in the author’s work was considered a three-dimensional
  diffeomorphism and it was assumed that all the eigenvalues of the Jacobi matrix at the origin are real.
  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. In the present paper we consider the diffeomorphism a three-dimensional space and it is
  assumed that the Jacobi matrix at the origin has complex eigenvalues. It is shown that in this case the
  neighborhood nontransversal homoclinic point can contain an infinite number of stable periodic points
  with characteristic exponents bounded away from zero. Refs 8.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при 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 4 (62); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: three-dimensional diffeomorphism
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: hyperbolic point
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.title
metadata.value: To the question of stability of periodic points of three-dimensional diffeomorphisms
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 02-Vasiljeva.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/6941/1/02-Vasiljeva.pdf
resources.format: Adobe PDF
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