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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bifurcation of homoclinics


Author: Jacobo Pejsachowicz
Journal: Proc. Amer. Math. Soc. 136 (2008), 111-118
MSC (2000): Primary 34C23, 58E07; Secondary 37G20, 47A53
Published electronically: September 27, 2007
MathSciNet review: 2350395
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Abstract: We show that homoclinic trajectories of nonautonomous vector fields parametrized by a circle bifurcate from the stationary solution when the asymptotic stable bundles of the linearization at plus and minus infinity are ``twisted'' in different ways.


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Additional Information

Jacobo Pejsachowicz
Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Email: jacobo.pejsachowicz@polito.it

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09088-0
PII: S 0002-9939(07)09088-0
Keywords: Differential equations, homoclinics, bifurcation, index bundle
Received by editor(s): August 3, 2006
Published electronically: September 27, 2007
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2007 American Mathematical Society