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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 of Hamiltonian systems


Author: Jacobo Pejsachowicz
Journal: Proc. Amer. Math. Soc. 136 (2008), 2055-2065
MSC (2000): Primary 37J45, 58E07; Secondary 34C37, 58J30, 53D12
Published electronically: February 20, 2008
MathSciNet review: 2383511
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Abstract: We obtain sufficient conditions for bifurcation of homoclinic trajectories of nonautonomous Hamiltonian vector fields parametrized by a circle, together with estimates for the number of bifurcation points in terms of the Maslov index of the asymptotic stable and unstable bundles of the linearization at the stationary branch.


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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/S0002-9939-08-09342-8
PII: S 0002-9939(08)09342-8
Keywords: Bifurcation, Hamiltonian systems, homoclinic trajectories, spectral flow, Maslov index
Received by editor(s): February 9, 2007
Published electronically: February 20, 2008
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2008 American Mathematical Society