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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