Title: Bifurcation from a homoclinic orbit in parabolic differential equations
Abstract: Synopsis This paper considers autonomous parabolic equations which have a homoclinic orbit to an isolated equilibrium point. We study these systems under autonomous perturbations. Firstly we prove that the perturbation under which the homoclinicorbit persists forms a submanifold of codimension one. Then, if a perturbation of this manifold is considered, we prove that a unique stable periodic orbit arises from the homoclinic orbit under certain conditions for the eigenvalues of thesaddle point.
Publication Year: 1986
Publication Date: 1986-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 16
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