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Stable Periodic Solutions of Periodic Systems of Differential Equations

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Abstract

An infinitely differentiable periodic two-dimensional system of differential equations is considered. It is assumed that there is a hyperbolic periodic solution and there exists a homoclinic solution to the periodic solution. It is shown that, for a certain type of tangency of the stable manifold and unstable manifold, any neighborhood of the nontransversal homoclinic solution contains a countable set of stable periodic solutions such that their characteristic exponents are separated from zero.

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7–9, St. Petersburg, 199034, Russia

    E. V. Vasil’eva

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  1. E. V. Vasil’eva
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Correspondence to E. V. Vasil’eva.

Additional information

Original Russian Text © E.V. Vasil’eva, 2018, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2018, Vol. 63, No. 1, pp. 13–19.

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Vasil’eva, E.V. Stable Periodic Solutions of Periodic Systems of Differential Equations. Vestnik St.Petersb. Univ.Math. 51, 9–14 (2018). https://doi.org/10.3103/S1063454118010119

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  • DOI: https://doi.org/10.3103/S1063454118010119

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