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Bifurcation from a homoclinic orbit in parabolic differential equations

Published online by Cambridge University Press:  14 November 2011

C. Miguel Blázquez
C. Miguel Blázquez
Affiliation:
Brown University, Division of Applied Mathematics, Providence, R. I. 02912, U.S.A.
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 3-4 , 1986 , pp. 265 - 274
Copyright
Copyright © Royal Society of Edinburgh 1986

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