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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Periodic Systems of Differential Equations with Infinite Set of Stable Periodic Solutions

Author(s):

Ekaterina Viktorovna Vasileva

Assoc.Prof.
St.Petersburg State University,
Universitetski pr. 28,
St Petersburg, Russia

ekvas1962@mail.ru

Abstract:

Periodic systems of differential equations with a hyperbolic periodic solution and non-transversal homoclinic solution are considered. In the works of S. Newhouse, L. P. Shil’nikov, B. F. Ivanov it has been shown that under certain conditions on the type of contact of the stable and unstable manifolds, the neighborhood of the homoclinic solution may contain a countable set of stable periodic solutions, but at least one of their characteristic exponents tends to zero when period increasing. The goal of this work is to prove that under certain conditions imposed on the character of tangency between the stable and unstable manifolds, the neighborhood of the homoclinic solution may contain a countable set of stable periodic solutions whose characteristic exponents are negative and bounded away from zero. References 36 w.

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