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arXiv:1406.3760 [math.DS]AbstractReferencesReviewsResources

Spectral flow, crossing forms and homoclinics of Hamiltonian systems

Nils Waterstraat

Published 2014-06-14, updated 2015-11-01Version 2

We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable and unstable subspaces, respectively. Finally, we deduce sufficient conditions for bifurcation of homoclinic trajectories of one-parameter families of nonautonomous Hamiltonian vector fields.

Comments: 35 pages; v2: final version, Theorem 2.7 improved according to referee's suggestions, additional minor changes
Journal: Proc. Lond. Math. Soc. (3) 111, 2015, 275-304
Categories: math.DS, math.DG, math.FA, math.SG
Subjects: 58J30, 37J45, 58E07
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