Spectral flow, crossing forms and homoclinics of Hamiltonian systems

Abstract

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.

35 pages; v2: final version, Theorem 2.7 improved according to referee's suggestions, additional minor changes

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