title: Stability of periodic points of diﬀeomorphism of a plane in the case of a homoclinic orbit
metadata.name: dc.contributor.author
metadata.value: Vasileva, Ekaterina V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-05-24T08:15:37Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-05-24T08:15:37Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vasileva E.V. Stability of periodic points of diffeomorphism of a plane in the case of a homoclinic orbit. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 1, pp. 44–52.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.103
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15536
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We consider a diﬀeomorphism of a plane into itself with a ﬁxed hyperbolic point at the origin and a non-transversal homoclinic point to it. Periodic points lying in a suﬃciently small neighborhood of the homoclinic point are divided into single-pass and multi-pass, depending on the location of the orbit of the periodic point with respect to the orbit of the homoclinic point. From the works of S. Newhouse, L. P. Shil’nikov, B. F. Ivanov and a number of other authors it follows that for a certain method of tangency of the stable and unstable manifold an arbitrarily small neighborhood of the nontransversal 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. From the previous works of the author it follows that for the other method of tangency of the stable and unstable manifold, an arbitrarily small neighborhood of the nontransversal homoclinic point can contain an inﬁnite set of stable single-pass periodic points. Characteristic exponents of these points are separated from zero. In this paper it is shown that under certain conditions imposed, ﬁrst of all, on the method of tangency of the stable and unstable manifold, an arbitrarily small neighborhood of the nontransversal homoclinic point can contain a countable set of multi-pass (exactly two-pass) stable periodic points. Characteristic exponents of these points are 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 6 (64); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: diffeomorphism of the plane
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: Stability of periodic points of diﬀeomorphism of a plane in the case of a homoclinic orbit
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 44-52.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15536/1/44-52.pdf
resources.format: Adobe PDF
resources.size: 284,05 kB