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Поле DC | Значение | Язык |
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dc.contributor.author | Vasil’eva, Ekaterina V. | - |
dc.date.accessioned | 2021-07-16T14:45:26Z | - |
dc.date.available | 2021-07-16T14:45:26Z | - |
dc.date.issued | 2021-06 | - |
dc.identifier.citation | Vasil’eva E.V. Different types of stable periodic points of diffeomorphism of a plane with a homoclinic orbit. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 2, pp. 295–304. | en_GB |
dc.identifier.other | https://doi.org/10.21638/spbu01.2021.209 | - |
dc.identifier.uri | http://hdl.handle.net/11701/29884 | - |
dc.description.abstract | A diffeomorphism of the plane into itself with a fixed hyperbolic point is considered; the presence of a nontransverse homoclinic point is assumed. Stable and unstable manifolds touch each other at a homoclinic point; there are various ways of touching a stable and unstable manifold. In the works of Sh. Newhouse, L. P. Shilnikov and other authors, studied diffeomorphisms of the plane with a nontranverse homoclinic point, under the assumption that this point is a tangency point of finite order. It follows from the works of these authors that an infinite set of stable periodic points can lie in a neighborhood of a homoclinic point; the presence of such a set depends on the properties of the hyperbolic point. In this paper, it is assumed that a homoclinic point is not a point at which the tangency of a stable and unstable manifold is a tangency of finite order. Allocate a countable number of types of periodic points lying in the vicinity of a homoclinic point; points belonging to the same type are called n-pass (multi-pass), where n is a natural number. In the present paper, it is shown that if the tangency is not a tangency of finite order, the neighborhood of a nontransverse homolinic point can contain an infinite set of stable single-pass, double-pass, or three-pass periodic points with characteristic exponents separated from zero. | en_GB |
dc.description.sponsorship | The work is supported by Russian Foundation for Basic Research (grant no. 19-01-00388). | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 8 (66); Issue 2 | - |
dc.subject | diffeomorphism | en_GB |
dc.subject | nontransverse homoclinic point | en_GB |
dc.subject | stability | en_GB |
dc.subject | characteristic exponents | en_GB |
dc.title | Different types of stable periodic points of diffeomorphism of a plane with a homoclinic orbit | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 2 |
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Файл | Описание | Размер | Формат | |
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295-304.pdf | 305,38 kB | Adobe PDF | Просмотреть/Открыть |
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