# Spectral Flow and Bifurcation of Critical Points of Strongly Indefinite Functionals

@article{Fitzpatrick2000SpectralFA, title={Spectral Flow and Bifurcation of Critical Points of Strongly Indefinite Functionals}, author={Patrick M. Fitzpatrick and Jacobo Pejsachowicz and L'azaro Recht}, journal={Journal of Differential Equations}, year={2000}, volume={163}, pages={18-40} }

Abstract Our main results here are as follows: Let X λ be a family of 2 π -periodic Hamiltonian vectorfields that depend smoothly on a real parameter λ in [ a , b ] and has a known, trivial, branch s λ of 2 π -periodic solutions. Let P λ be the Poincare map of the linearization of X λ at s λ . If the Conley–Zehnder index of the path P λ does not vanish, then any neighborhood of the trivial branch of periodic solutions contains 2 π -periodic solutions not on the branch. Moreover, if each…

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