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This Research Note explores existence and multiplicity questions for periodic solutions of first order, non-convex Hamiltonian systems. It introduces a new Morse (index) theory that is easier to use, less technical, and more flexible than existing theories and features techniques and results that, until now, have appeared only in scattered journals.

Morse Theory for Hamiltonian Systems provides a detailed description of the Maslov index, introduces the notion of relative Morse index, and describes the functional setup for the variational theory of Hamiltonian systems, including a new...

This Research Note in Mathematics 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. This text provides an accessible, self-contained treatment of the subject matter 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.

Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics.  The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.