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dc.contributor.authorVasil’eva, Ekaterina V.-
dc.identifier.citationVasil’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.description.abstractA 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.sponsorshipThe work is supported by Russian Foundation for Basic Research (grant no. 19-01-00388).en_GB
dc.publisherSt Petersburg State Universityen_GB
dc.relation.ispartofseriesVestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 8 (66); Issue 2-
dc.subjectnontransverse homoclinic pointen_GB
dc.subjectcharacteristic exponentsen_GB
dc.titleDifferent types of stable periodic points of diffeomorphism of a plane with a homoclinic orbiten_GB
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