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http://hdl.handle.net/11701/33257
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Поле DC | Значение | Язык |
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dc.contributor.author | Vasil’eva, Ekaterina V. | - |
dc.date.accessioned | 2021-10-07T11:44:19Z | - |
dc.date.available | 2021-10-07T11:44:19Z | - |
dc.date.issued | 2021-09 | - |
dc.identifier.citation | Vasil’eva E.V. Multi-pass 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 3, pp. 406–416. | en_GB |
dc.identifier.other | https://doi.org/10.21638/spbu01.2021.303 | - |
dc.identifier.uri | http://hdl.handle.net/11701/33257 | - |
dc.description.abstract | A diffeomorphism of a plane into itself with a fixed hyperbolic point and a nontransversal point homoclinic to it is studied. There are various ways of touching a stable and unstable manifold at a homoclinic point. Periodic points whose trajectories do not leave the vicinity of the trajectory of a homoclinic point are divided into a countable set of types. Periodic points of the same type are called n-pass periodic points if their trajectories have n turns that lie outside a sufficiently small neighborhood of the hyperbolic point. Earlier in the articles of Sh. Newhouse, L. P. Shil’nikov, B. F. Ivanov and other authors, diffeomorphisms of the plane with a nontransversal homoclinic point were studied, it was assumed that this point is a tangency point of finite order. In these papers, it was shown that in a neighborhood of a homoclinic point there can be infinite sets of stable two-pass and three-pass periodic points. The presence of such sets depends on the properties of the hyperbolic point. In this paper, it is assumed that a homoclinic point is not a point with a finite order of tangency of a stable and unstable manifold. It is shown in the paper that for any fixed natural number n, a neighborhood of a nontransversal homolinic point can contain an infinite set of stable n-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 3 | - |
dc.subject | diffeomorphism of plane | en_GB |
dc.subject | nontransversal homoclinic point | en_GB |
dc.subject | stability | en_GB |
dc.subject | characteristic exponents | en_GB |
dc.title | Multi-pass stable periodic points of diffeomorphism of a plane with a homoclinic orbit | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 3 |
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Файл | Описание | Размер | Формат | |
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406-416.pdf | 313,04 kB | Adobe PDF | Просмотреть/Открыть |
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