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Bifurcation of a unique stable periodic orbit from a homoclinic orbit in infinite-dimensional systems

Authors: Shui-Nee Chow and Bo Deng
Journal: Trans. Amer. Math. Soc. 312 (1989), 539-587
MSC: Primary 58F14; Secondary 34G20, 34K15, 35B32, 35R20
MathSciNet review: 988882
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Abstract: Under some generic conditions, we show how a unique stable periodic orbit can bifurcate from a homoclinic orbit for semilinear parabolic equations and retarded functional differential equations. This is a generalization of a result of Šil'nikov for ordinary differential equations.

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Article copyright: © Copyright 1989 American Mathematical Society

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