Morse Theory for Hamiltonian Systems

This Research Note introduces a new Morse (index) theory that is easier to use, less technical, and more flexible than existing theories for strongly indefinite functionals. It also contains an extensive survey of material that is now classical but has never appeared in book form. Until now, these results have appeared only in scattered journals. Requiring few prerequisites, the author has developed an accessible, self-contained treatment with full proofs of the major results and complete with applications of the theory to Hamiltonian systems and other areas of current research, including wave equations, Chern-Simon functionals, and Lorentzian geometry.