Stable Periodic Solutions of Periodic Systems of Differential Equations
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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.
Keywordsnontransversal homoclinic solution stability characteristic exponents
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- 3.S. Smale, “Diffeomorfisms with many periodic points,” in Differential and Combinatorial Topology (Princeton Univ. Press, Princeton, NJ, 1965), pp. 63–80.Google Scholar