title: Stability of periodic points of diffeomorphisms of multidimensional space
metadata.name: dc.contributor.author
metadata.value: Vasilieva, Ekaterina V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-09-18T11:24:58Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-09-18T11:24:58Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vasilieva E.V. Stability of periodic points of diffeomorphisms of multidimensional space. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 3, pp. 356–366.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.302
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/14881
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We study a diffeomorphism of a multidimensional space into itself with a hyperbolic fixed
  point at the origin and a non-transversal homoclinic to it point. From the works of Sh. Newhouse,
  B. F. Ivanov, L. P. Shilnikov and other authors it follows that under a certain method of tangency of the stable and unstable manifolds, a neighborhood of a non-transversal homoclinic
  point can contain an infinite set of stable periodic points, but at least one of the
  characteristic exponents of these points tends to zero with increasing period. In this paper,
  we study diffeomorphisms for which the method of tangency of the stable and unstable
  manifolds differs from the case studied in the works of the above-mentioned authors. This
  paper is a continuation of the author’s previous works, in which diffeomorphisms were
  studied, whose Jacobi matrices at the origin had only real eigenvalues. Conditions were
  obtained under which the neighborhood of a non-transversal homoclinic point of such diffeomorphism
  contains an infinite set of stable periodic points with characteristic separated
  from zero. In this paper, it is assumed that the Jacobi matrix of the original diffeomorphism
  at the origin has not only real eigenvalues, but also a non-unique pair of complex
  conjugate eigenvalues. Under this assumption, conditions are obtained for the presence in
  the neighborhood of a non-transversal homoclinic point of an infinite set of stable periodic
  points with characteristic exponents separated from zero.
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 5(63); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: multidimensional diffeomorphism
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: hyperbolic point
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: non-transversal homoclinic point
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stability
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stability of periodic points of diffeomorphisms of multidimensional space
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/11701/14881/1/02-Vasiljeva.pdf
resources.format: Adobe PDF
resources.size: 301,73 kB