title: Multidimensional diffemorphisms with stable periodic points
metadata.name: dc.contributor.author
metadata.value: Vasil’eva, Ekaterina V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-12-06T12:01:14Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-12-06T12:01:14Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vasil’eva E.V. Multidimensional diffemorphisms with stable periodic points. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 4, pp. 608–618.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.406
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16743
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Diffeomorphisms of a multidimensional space into itself with a hyperbolic fixed point are
  considered, it is assumed that at the intersection of the stable and unstable manifolds there
  are points that are different from the hyperbolic, such points are called homoclinic. The
  homoclinic points are divided into transversal and non-transversal, depending on the behavior
  of stable and unstable manifolds. From the articles of S. Newhouse, L. P. Shil’nikov,
  B. F. Ivanov and other authors, it follows that with a certain method of tangency of the stable
  manifold with unstable one at the homoclinic point, a neighborhood of a non-transversal
  homoclinic point contains an infinite number of stable periodic points, but at least one of
  the characteristic exponents at these points tends to zero with increasing period. The proposed
  work is a continuation of the work of the author. In previously published papers,
  restrictions were imposed on the eigenvalues of the Jacobi matrix of the original diffeomorphism
  at a hyperbolic point. More precisely, in these papers it was assumed that either
  all eigenvalues are real and the matrix is diagonal, or the Jacobi matrix has only one real
  eigenvalue modulo less than one, and all other eigenvalues are different complex integers
  modulo greater than unity. Under these conditions, conditions are obtained for the presence
  in an arbitrary neighborhood of a non-transversal homoclinic point of an infinite set
  of stable periodic points with characteristic exponents separated from zero. In this paper,
  it is assumed that the Jacobi matrix of a diffeomorphism has an arbitrary set of eigenvalues
  at a hyperbolic point. In this case, the conditions of existence in the neighborhood of the
  non-transversal homoclinic point of an infinite set of stable periodic points, whose characteristic
  exponents are separated from zero, are obtained. The conditions are imposed, first
  of all, on the method of tangency of the stable manifold with unstable one; however, in the
  proof of the theorem, the properties of the eigenvalues of the Jacobi matrix at a hyperbolic
  point are essentially used.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The article was prepared with the financial support of the Russian Foundation for Basic Research (RFBR), project 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 6 (64); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: multidimensional diffeomorphism
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.subject
metadata.value: characteristic exponents separated from zero
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Multidimensional diffemorphisms with stable periodic points
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 608-618.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16743/1/608-618.pdf
resources.format: Adobe PDF
resources.size: 291,1 kB