Stable Periodic Solutions of Periodic Systems of Differential Equations

Mathematics
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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.

Keywords

nontransversal homoclinic solution stability characteristic exponents 

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Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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